First off, the OP was talking about Busch Gardens.
There's a reason we all love Disney.
A couple of months ago I looked for information about Six Flags and found out they don't have anything like a GAC. Used to, too many abusers, got rid of it. Which they can do if they want. And we can choose not to give them our business.
I think that a big problem is that because of ADA you don't have to show proof of disability. Now before I get pummelled by rocks

let me explain. I understand our right to privacy. I understand that somebody could fake a doctor's note. I understand that park employees (
any park) are not trained medical professionals. However, not having to show proof means that if you're smart and creative you can work the system. And that hurts us all.
This would be my suggestion: make applying for a GAC something that needs to be done in advance. (I honestly don't believe that most people needing accomodation just "show up" at Disney without doing any prep work at all) An application that needs to be signed off by a doctor or psych. The form could be returned in advance and your name put into the computer system for your arrival. That would also take the guess-work out of the GAC depending on who was working at Guest Relations that day, the forms could all go to a central location and processed by someone who knows more.
That's the way it works if you need 504 accomodations at, say, a college. There is a form that has to be filled out if you want accomodations, and while it's possible to "fake" it I guess, it doesn't happen very often at all. Because it's complicated enough that most fakers won't go to the trouble. The form will include a checklist of all the possible GAC accomodations, which will not include FOTL. The guest will know in advance that they won't get FOTL. But a college's 504 form also has the doctor write down the official diagnosis, the last time that evals were done, etc.
Now, sure there will be doctors that will fill one out for people that don't need it. My MIL's doctor keeps filling out a form to let her keep her driver's license that she shouldn't have.

But most doctors (read: the ones with ethics) would tell the truth.
If a guest is wheelchair or
scooter, they wouldn't need to do the form as long as they understand what they're getting into. If they need accomodation beyond that, here's the form.
That's just my idea, of course. Not that it would be perfect, but it might be better than what exists now. I think any of us on this board, if we had taken such a form to the doctor, they would have filled it out for us no problem and likely the same accomodations we'd needed.
What happened to the OP is really sad. An employee who was obviously under-trained and in too much of a rush to listen to a guest. Another guest who perhaps was abusing the system, but more than that was obnoxious. So many people have a warped sense of entitlement, and it's getting worse and worse, about almost everything. But those people know they're not really entitled, which is why they feel the need to pass judgement on others, so that the finger doesn't point at them. Sounds like maybe that's what happened.