The part nobody spells out
Why the task, not the paperwork, creates access
Public access does not come from a card, a vest, a registry entry or a letter. It comes from the animal doing trained work connected to a disability. That is the whole basis of it, and understanding this saves people from buying things that cannot deliver what they promise.
It also accounts for a rule handlers find odd. Precisely two things may be asked of you in a shop: whether disability accounts for the dog, and what it has learned to do. They may not ask about your condition and may not demand documents. The questions probe the work, because the work is the qualifying fact.
The corollary is uncomfortable but worth stating. A dog that cannot perform reliably in the environment where you need it has not yet earned that access, whatever you have paid or been told. Training is not a formality standing between you and a right; it is the thing itself.