I trained him, however I did so after almost 20 years as a qualified trainer, and I started with a scent hound which made it significantly more likely he would naturally indicate without training.
From there I built on his skills so offering him samples of blood/saliva/breath, and rewarding the right indication for the right samples (to my knowledge he's never actually been wrong but we had to wait whilst my condition changed to teach him about hypos, hypers were easy as I had them a lot).
He's actually my second but my first girly died suddenly aged two so by the time he'd arrived id already spent nearly 2 years bringing on and training an assistance dog (same breed) so it was just typical daily life at that point.
Public access work is a matter of having that in mind when socialising/habituating a puppy, so we were careful NOT to let all and sundry greet him and started early on with one harness for 'work' (at that point simply 'not greeting strangers') and one for 'not work' where he could meet people.
We're lucky here that loads of stores would let him in to train with prior permission so he got to practice 'ignore the people' and actually the hardest part of training him has been 'you do NOT need to tell everyone else about their blood sugars thanks!' but as we got the 'we don't talk to strangers' lesson in really early, it was only friends he'd try this with.
DPT again is easy, the breed are known for being keen on close contact and cuddles so a case of reinforcing it when offered, then putting it on cue and making it specific to me and his natural willingness to offer it when I spasm anyway.
Once we got to where I thought he was good, I took him through the ADUK criteria for public access (its just a suggested list of skills) and had another trainer observe him tasking and coping with those set situations.
The downsides of his breed are that he is hairy and dribbly, so everywhere we go he has to be brushed out well before hand and we take a cloth. He is also long in the back with a long tail, and not overly great at tidying himself away so I would not take him on public transport unless I absolutely had to.
There are now lots of trainers assisting owner-trainers, I have done a bit myself before I retired from physical training - but it DOES concern me that there are people attempting to owner-train without outside assistance, when their health issues mean they are struggling to do the thing they are teaching their dog to do (particularly anxiety based stuff!) and then there are the people who have got wholly unsuitable dogs having put their preference for that breed above the need for the dog to do the job!
If you are a business - you CAN ask a team to leave if you have strong reason to believe they are a danger to you/staff/other shoppers as a result of the handlers or dogs behaviour - so dog off lead, growling at other dogs, barking at or lunging at passers by (caveat SOME dogs are taught to find a human and alert them but this is rare and you'd generally know as there dog would be asking you to follow so perhaps barking and turning away to take you to their person).
Obviously you'd be standing on no legs if your decision is based on 'someone might have a dog allergy' or 'that dog looks like a dodgy breed I don't like'.
I'd also say there is a strong case for asking someone with a filthy muddy minging dog to leave whilst they clean up their dog - shedding hair is unavoidable but expecting to bring a dog dropping visible mud/foxpoo/filth everywhere is not!