This reminds me of the controversy last year over "Miss Manners" and her advice that we should just run to the bathroom to test our bood sugar or inject.
Personally, I think the question and response are not inappropriate. If she is squeemish she can ask to be moved. But she certainly should not be allowed to compromise the workers rights to reasonable accommodation to test and inject when needed.
Personally I also think it is a two way street. If someone get's squeemish I am all to happy to tell them I am about to inject so that they can run off to the bathroom.