Fargo is a black comedy. Considering that the likes of Driving Miss Daisy and Ghost were classified as comedies by the Golden Globes, I think that it (and The Martian) are perfectly justifiable.

I think the category change was just a way to get it nominated. Maybe there weren't enough slots in the drama section to include it, but the nominators still wanted it to have a shot at best movie so they figured, "Hey, it's sort of a dark comedy isn't it? I mean, I laughed a few times during it so maybe it is a comedy and we can nominate it as such?" I'm sad it didn't win though.
That genre labeling is what kind of messed up my expectations the first time I saw it in like 2000 or so. I thought it was gonna be hilarious because it was described as a comedy and it wasn't.
Same goes for The Martian, nominators probably didn't see it having a chance against Leo and the Bear, but they still wanted The Martian to have a shot at winning. So, since they laughed a few times during the movie, boom, best comedy.
TL,DR: I want ice cream.