They're going to be accused of wanting the special and unique stamp in either case, but at least in the second one they can feel somewhat comfortable.
People will, of course, conjure up an unreasonable accommodation (in an attempt to paint all accommodations as unreasonable) in their head to try to justify why this sort of request can't be accommodated, which just increases the fuel for the desire to get the autism diagnosis.
Put another way, if people were a little more accepting, less only-slightly-weird people would be seeking these diagnoses.