I had a very embarrassing experience involving the handicapped stall once that I'm still not entirely sure what to make of.
I won't get into the TMI details here, but long story short, I legitimately needed to be in a bathroom stall for a few minutes longer than the standard, expected time. This was in a fast food place. I always feel somewhat guilty already whenever this happens because of taking up so much time, but in this case I did not feel nearly so bad, because there were, in fact, two stalls. One regular and one handicapped. So, I went into the regular stall, and...began the proceedings.
Almost immediately after this, a woman walked into the bathroom, and just...stood there. Didn't knock, so I suppose it was clear that my stall was occupied. She just stood there, and stood there...even after over 5 minutes, and even though no one else came into the restroom, she just stood there.
Finally, when I finished my business and was washing my hands, she went into the stall I had been in and proceeded to do her own business. I felt really bad because she clearly had such strong feelings about not using the handicapped stall that she was waiting on mine! And I noticed she had on the uniform of the fast food place, so I wondered if she had just spent all of her break time waiting on me or what.
I still don't think I did the wrong thing. Had I known in advance what would happen, I would have used the handicapped stall instead. But I can't read minds. Odds were much better that a person in legitimate need of the handicapped version of a stall would have come in, than what actually happened, I think! But I still feel really weird about it.
Bottom line, I think some people take this handicapped stall thing, not too seriously, I wouldn't say, but seriously in the wrong way. So we get situations like mine, and like the OP's where somebody felt the need to not mind her own business. And I think the OP handled it very well! It wasn't anybody else's business if she was handicapped or not or what the nature of that handicap might be. Ms. Busybody got exactly the reaction she deserved.