Ahhh.
Well, in that case, recall that this is no different than if you were diabetic, or had RA or something like that. Yes, I suppose it IS a weakness-- but at the same time, if they have a need to know, they have a need to know.
You can't really control what they think about the information you're giving, though... so if they wind up thinking that you're um-- er--
a candy-***, I guess, for lack of a better term here--
are they REALLY people that you want in your life?
I realize that is sometimes a very painful calculus to engage in, but it does actually make things easier in the long run. A workplace which is hostile toward FA is one that either needs to be educated (via HR about how FA is, in point of fact, a disability vis a vis ADAA), or avoided.