The rule is that if you win on time but don't have the material to force a mate without the help of your opponents pieces, then the game is drawn. FIDE assumes that your opponent is competent enough to not give you a helpmate in that kind of situation.
Obscure Insufficient Material Ruling

FIDE assumes that your opponent is competent enough to not give you a helpmate in that kind of situation.
I think you will find FIDE rules would declare a win for Black. The relevant line from FIDE article 6.9 is " However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves"
"any possible series of legal moves" does not rule out a helpmate.
Under USCF rules the result would be a draw. Chess.com more closely follows USCF rules and the result on this site would be a draw.

FIDE assumes that your opponent is competent enough to not give you a helpmate in that kind of situation.
I think you will find FIDE rules would declare a win for Black. The relevant line from FIDE article 6.9 is " However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves"
"any possible series of legal moves" does not rule out a helpmate.
Under USCF rules the result would be a draw. Chess.com more closely follows USCF rules and the result on this site would be a draw.
I didn't know that, I just assumed FIDE and USCF had the same ruling in this matter.
Ignore my post, OP

That's how I read the rules.. not that a side must have material enough to force a mate, but to be able to mate with his opponent making the worst moves possible. So in the given case, if White ran out of time, I would guess that Black would win since mate is indeed a possibility with White's worst play.

As others have said, USCF calls it a draw if the side with low material and time remaining can't force mate and has insufficient mating chances, FIDE calls it a win if mate can be produced from the current position.
I was doing research on this topic today actually and came across this very interesting position:
http://www.chess.com/forum/view/game-analysis/how-is-this-drawn-by-insufficient-material
Black has KNN vs. White's KPP. White ran out of time, and the game was drawn by insufficient material, but according to tablebases, with best play from both sides, the game is a win for black in 47 moves. However, with chess.com's current programming, it fails to recognize forced wins with KNN (I assume it can't with KN or KB either). I'm sure there's a way to have it check tablebases in positions with fewer than six pieces remaining, but right now it's definitely not an optimal system.
Ok braniacs...try this one...
I am well-aware of the insufficient material rule.
W: K+p
B: K
will result in a win for W if black loses on time, but will result in a draw for black if W loses on time.
However, what about this?
W: K,p,p,p,p,R,N,B
B: K+B
It is impossible to mate with a K+B vs. K...but it is NOT impossible to mate (although impossible to force) with K+B versus a whole army for white if white is trapped by his own pieces.
Therefore, what happens if white loses on time? Does black get a win or a draw?
Please explain the official ruling on this obscure point.