Some jobs (usually ones that are physically demanding/strenuous/require fitness) might have new hires undergo a health screening, though. Don’t want to be sending someone to do underwater welding who suffers from respiratory issues, for example.
But in terms of history, you’re right, absolutely not. If it’s something that might just be sensitive/embarrassing but isn’t part of the job description, it’s none of their business.
Wouldn’t be my choice, but the thing about burgers is that you can basically do anything to them and no one will care.
Something about pizza is sacred; people get very defensive about regional varieties and makeup. Burgers are profane in comparison. I’m sure there’s a line to be drawn at some point for what a “wrong” burger is, but it’s a pretty far and blurry line.