Long time standard poodle owner here and I feel must speak in defence of them!
They are one of the two most intelligent breeds of dogs and so require firm and consistent training, but they do respond well to it. Because they're so intelligent, they require mental stimulation as well and this is why they can be so lively. They're not obsessively neurotic like collies though!
Remeber, they're all individuals! Not every standard is going to be hard work. As your parents are set on a standard, they should look for the calmest in a litter- and do their research! Check the poodle parents also have calm natures and ask as many questions as you need about the health & temperament of the bloodline.
Obedience classes are a must for them, I think, as first time dog owners and because standards grow up to be strong dogs - it's essential they get the training right from the start.
If they were my parents I'd absolutely share your concerns about the dog's strength so definitely invest in obedience training from the start.
They're not large to start with though, so your parents will have time to get a solid foundation in place.
Make sure they have their pup neutered and discourage behaviour such as jumping up to greet or in excitement from the start, however adorable it is in puppyhood. Unlike with smaller breeds, you can't afford to be relaxed with training just because 90% of the time they get it right and they're-such-a-lovely-boy/girl-and-not-being-naughty!
If your parents aren't responding to the idea that they might get pulled over, ask them how they would feel if their dog broke free and dashed into the path a vehicle.
Make sure they're ready for adolescence because, as with any dog, a standard may try to test boundaries so training may need to be reinforced during this stage.
Standards are very loving, have wonderful, gentle temperaments though and a great sense of humour.
I've only ever known them to be great and very gentle with children...but again, how would your parents feel if on a walk a child was accidentally knocked over?
On walks, however well behaved your dog might be, some people (and children) get very nervous around big dogs - especially if they're being exuberant, so while the dog may be behaving perfectly well, it's again important to perfect it's responses to commands (recall/sit/stay/leave etc)