You are SPOT on with this assessment.
I have celiacs disease, and more often then not (like 99% of the time), depending on the health of my gut at the moment, I can't handle a single breadcrumb without being deathly sick for a week. I stopped telling servers long ago that this was a Celiac issue since a lot of servers outside of Disney just never knew what it was. They'd look at me like I had 3 heads on my shoulder. So eventually I learned that telling them I had a "gluten allergy" was more universally understood and accepted. Eventually, it became habit for me when dining out. I'm sure others figured this out too.
I do hate seeing people order things saying they have an allergy if they don't though. For instance, I watched one woman in front of me in line at the food shack, at Typhoon Lagoon, go over all of the gluten free options with a chef that came out just for her. She talked with the chef about this for a good 20 minutes and was adamant that her allergy was bad. The chef was great, and reassured her on everything and said it would be prepared separately and safely. And then at the end, she said "screw it I'm on vacation, can I have the gluten filled cookie also?". I felt so bad for the chef, and myself at that moment lol. I was in disgust, and embarrassment, knowing I would be talking to that exact chef next and that he probably won't take me seriously now thanks to this woman in front of me. Of course he was great with me and I had no issues, but this kind of thing happens a TON I imagine.
I've never worked in a restaurant, but I pity servers having to deal with these situations. My fiance knows me so well, but even she doesn't understand fully the science of my Celiac issue. So I can only imagine what a server knows after their wild experiences with so many different people's requests with this kind of stuff.