To not understand what this parent was thinking?

Total twaddle!

the level of apprehension I’ve seen the OP have is similar to that I have about my muzzled dog biting someone who touches their mouth

Except your dog is muzzled and as such you have taken more precautions than OP. So... not similar at all.

The OP has not talked about having any reasonable apprehension that would meet the bar set out in law

The bar in law is set extremely low in these cases - and almost always sides against the owner, with whom it strictly places responsibility. She has admitted she wasn't paying attention, and she has admitted her dog is wary of children and as such she takes precautions around them. That is enough to acknowledge she is aware of a temperament issue, and that is enough for reasonable apprehension.

While the toddler's lack of supervision is a factor, UK law consistently holds that the ultimate responsibility for a dog's actions lies with the keeper who failed to prevent the interaction.

OP is trying to deflect her responsibility for what happened which unfortunately, the law says she cannot wave away.

OP was not paying attention to her surroundings. That's fact, otherwise the child would have gotten nowhere near.

I know she wants to blame the parent, I know you do too - and no one has said there's not blame there. But there is ALSO blame for OP, and trying to make out that she has zero responsibility here is willful fabrication.

The difference being the child isn't capable of instantly ripping the dogs neck apart, killing the dog in a minute or two.

Same reason why everyone should be aware of roads, but those with the car are much more responsible given the soggy bag of water and bacteria isn't likely to kill the person in the tons of metal travelling at speed.

Nobody was paying adequate attention it seems.

The parent should not have allowed the child to approach the dog. Obviously.

OP should not have allowed her dog to become potentially distressed by allowing an unsupervised child to approach so close. She and her daughter could have blocked the child’s approach a bit earlier and/or led the dog away before the child was in his face.

Correction.
The parent wasn't paying attention and allowed their child to get nose to nose with a dog. It doesn't matter if the dog is wary or the best behaved, most placid dog in the world. A responsible parent does not let their child get in the face of ANY dog, of known temperament or not.
OP was watching her dog. It clearly didn't react or behave poorly or OP would have seen it as she was focused on the dog.
The parent should have been watching her child instead of outsourcing that to a slightly older one and OP.

You must have read a different thread to me, as the level of apprehension I’ve seen the OP have is similar to that I have about my muzzled dog biting someone who touches their mouth - it’s remote, but possible and I take steps to make sure it doesn’t happen and assume the broader public will also take sensible precautions.

The OP has not talked about having any reasonable apprehension that would meet the bar set out in law, she only talks about her anxious daughter being worried, and the definition of reasonable apprehension wouldn’t be set at the level of someone who has mental health issues related to being overly apprehensive.

The law isn't that stupid, that you could shove your fingers into the mouth of a dog and might get bit while it is wearing a muzzle, is not a "reasonable" apprehension it will injure someone.

Reasonable is a known and applicable concept in law.

That a child, that can be gone in an instant and doing child things as a very normal event in life, being around and close to the dog doing that normal thing is a concern and can cause aggression is a reasonable apprehension. Anyone she let's know the truth about the dog, would be concerned about it harming someone, regardless of of it does when out and about.

It is certainly easier to ignore uncomfortable facts that place you in the wrong, so I see why you're advising this, it's human nature.

It's especially difficult when you thought you were right, but have been shown quite publicly that's not the case. So OP does have my sympathies there.

I’d like to think that if someone had a dog that they knew could bite a young child they would have that dog muzzled or only take them to areas where the likelihood of encountering young kids would be minimal to none.

OP I'm not sure I'd continue to feed some of these posters if I were you. They either can't or don't want to see sense.

Where has she ignored her responsibilities!?!

She wasn't paying attention and allowed an unsupervised child to get close enough to be nose to nose with her wary dog.

This has been answered many times by many posters.

Where has she ignored her responsibilities!?! OP has taken very sensible precautions. There were two people on the walk. They were right there with him. She seems very knowledgeable about her dogs behaviour and body language and she and her daughter handled the situation in a way that didn't escalate anything. They were doing everything you said they should except muzzling.

And if, as you pointed out, "any" dog can attack (and I do agree with you) then by your logic, all dogs should be muzzled in public, shouldn't they? People see a big dog and they cross the road. That's not OP's problem or responsibility. It's not indicative if his behaviour. Where have you got the idea that he's dangerous and/or that OP is not capable of managing him?

Why is the dog getting any blame at all for this incident? It often amazes me how stupid parents can be. Children should be kept away from dogs unless it is clear that they will welcome attention.

OP, I commend your patience in explaining things ad infinitum to posters who seem intent on blaming you for somebody’s inability to parent. The reason, as far as I can gather, that you don’t 100% trust your dog if a toddler came up and poked him in the face is that he is a dog, and no dog on earth can be trusted 100%. If somebody poked me in the face, I’d probably bite them… And no, dogs don’t bite out of nowhere - as you say, there’ll have been warning signs that most people don’t notice or ignore (‘Aw look, he’s wagging his tail so he must be happy’ / ‘he’s yawning so he must be tired’ etc)

In summary: yes, that was completely unreasonable behaviour from the mother, who should have been watching her child.

Horrible people!

The OP has been clear along that her point was the child was lucky it was her under control dog they approached, not a less well trained one.

And a muzzle wouldn’t remove the apprehension, as if a toddler sticks its fingers into the muzzle, the dog can still bite so OP would be still have been apprehensive.

Why is it OP's responsibility to ensure a useless parent needs to actually parent their child ? Her dog is her responsibility, not other peoples children.

Oh he's beautiful !

For being a responsible and sensible dog owner, presumably :-)

Another young lady just 19 years old was killed last night by the family lurcher pet. The grandmother commented on the news posts saying the dog used to sleep in bed with the young girl and had never been aggressive before. Completely unprovoked and out of nowhere. How horrific. When will people wake up to that it’s not only dogs who have been abused or antagonised that react and snap. My sister also owned 2 boxer dogs whom she had from puppies, never been abused or mistreated in the slightest, used to run free round the farm at the horse stables every day so had regular exercise and weren’t cooped up all day. One day again out of nowhere one of them bit my niece in the face tearing her lip apart, she was just 18 months old. My sister was right there when it happened, the dog hadn’t been left alone with my niece either. The dogs had never been aggressive. There’s not always a “reason” dogs attack, reason being negative experiences or mistreatment.

You do know what the legal definition for a dangerously out of control dog it right?

It is, word for word from the legislation; "a dog shall be regarded as dangerously out of control on any occasion on which there are grounds for reasonable apprehension that it will injure any person [F2or assistance dog], whether or not it actually does so".

You made it clear you had a reasonable apprehension it could, for whatever reason which is irrelevant, potentially hurt the child doing normal child things out of "fear". A muzzle would remove this reasonable apprehension.

I agree with other posters in that it does sound like you might benefit from gaining some more info on how to protect your dog and others around you. Muzzling doesn’t sound a bad suggestion.

No-one is suggesting the child should have done what it did, but also, your Rottweiler x that people cross the road to avoid, shouldn’t ever be able to be in a position where it could kill a child that spooked it. Another dog death today. That’s two in two days. Dogs can and do kill.

Also, maybe ask your delete your photo as you’re identifiable and someone may report you