My impression was that people should be allowed to claim whatever they want.
In a situation like you have described, a mafia member would have two options:
1. Refuse to claim mafia.
2. Claim mafia and comply with the exploit.
In a situation like this, to not comply with the plan would be to reveal yourself as mafia - you don't want to be modkilled. Therefore, in order to not gamethrow, a mafia member should claim mafia and remain hidden (and then "admit" to actually being civvy once the plan is resolved.)
Mafia players who claim mafia in this situation are not gamethrowing and are remaining hidden. Mafia players who refuse to comply with the exploit to avoid being modkilled are essentially outing themselves as mafia, and are hence gamethrowing.
TL;DR: no