I think it would be beneficial, especially to newcomers, if there was some sort of icon in the specialist description that denotes a global ability. Or perhaps more practical is an icon to denote when the specialist needs to be present for the ability to take effect. Alternatively, you could just edit the ability descriptions to be more explicitly defined.
I've introduced a few people to the game, and this is a point of confusion with nearly all of them. They all get stuck on deciphering whether or not the ability has a global effect.
UPDATE: they have added "global" and "local" to the official documentation. thanks!
http://play.subterfuge-game.com/docs/Rulebook/Specialists.html