“Your argument is fallacious because X is not a central category member. And it’s not a central category member because…I say so?”
In my view, part of what makes the non-central argument a fallacy is the ad hoc use of the ‘overly restrictive definition’.
Whoever argues that “MLK is a criminal” with the intent of instilling the negative connotation of the term is unlikely to apply the same standard everywhere.
One in that case could reply that anyone who ever opposed any non-democratic regime and was found guilty of sedition/instigation/etc.… is/was also a criminal.
If the proponent of the argument disagrees, we fall into a contradiction. If in favour of the extended use, the original concept—criminal—is stripped off its stereotypical baggage.
An anecdote from which I drew a similar conclusion to yours:
About ten years ago I went with my dad to a music hall where a local marching band was playing. I play a few instruments, have a solid grasp of music theory, etc..., but I’m no professional, while he has ‘average Joe’ music training.
I found the concert to be genuinely painful to listen to: entire sections not in tune with each other, very poor dynamics (brass way too loud, woodwinds barely audible), melodies all over the place, sudden tempo changes etc...
After the last piece, the audience asked for the encore. I figured it had to do with social pressure/convention/kindness. Before I could say anything, my dad proceeded to extol the band’s musicianship and high level of the performance, assuming I too had enjoyed the experience.
I was (and still am) baffled.