IMO, there are lots of things that can make a campaign "gritty." You can lower the stats, limit the amount of magic, ratchet up the deadliness, etc. Sure, in the right setting (e.g., invasion of the flumphs), even these tricks won't make for a gritty game, but in most cases, they'll help.
As far as stats go, if you're looking for grit, I think that the best way to go is with a low point buy (say 20 or 22). As others have noted, rolling a bunch of 3d6's, especially if you can't arrange them to suit, doesn't give the player much control - you have the dice, rather than the player dictating the character concept. On the other hand, even with a low point-buy I can say, "ok, my guy is pretty smart (int 14) and likable (cha 12), and more or less average in every other way (straight 10's, with maybe an 8 thrown in)."
To return to Cthulu as an example, if you read the Lovecraft stories, in most cases the main characters are at least somewhat above-average in some way (smart, forceful personality, man of action, etc.) and often not noticeably below average in any area. The problem, of course, is that when a Shuggoth comes after you, it doesn't matter how strong, tough, or quick you are; you're still gonna get flattened.