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Might be because they're not a Northerner. They're First Men yeah, but their culture is Crannogman and the ambition triggers off that.

It's been a several patches since I tried that one though, too.
 
"First Men" aren't one of the "Seven Kingdoms"... well technically they are, but whatever.
 
The Vale's mountain clans are also First Men.
Right... Point being, Crannogmen and Northerners are both First Men, sure, but most importnatly they are both part of the North. Mountain clans and clawmen aren't part of the North. I mean hell, Free Folk are First Men too.
 
Well... then can't Crannogmen be counted as Northmen, Mountain Clansmen Valemen and Clawmen Crownlanders (if Crownlanders even count for the ambition at all, I can't remember right now).