[AaronBrown]

In addition to ohnonotthat's excellent reply I would add there is a deep and abiding superstition among blackjack players that bad play by other players at the table hurts the good players. Your friend has a relatively rational version of the superstition, I have heard much worse.

In general, it almost always helps the players slightly if another player hits. This is because the hit card gives them information, which they can use to their (slight) advantage. The dealer cannot use the information because her play is forced. You can construct examples where the hit causes a small disadvantage to other players, but they're unrealistic.

I think the superstition survives from the home game where the dealer does have choices. In most versions, it helps the dealer if a player busts, because the dealer is then free to optimize his play for the remaining players. So in home games, players will urge you not to hit anything that might bust, even if it's to your advantage to do so.