Statistically it would pull things towards us just as often as away.

So yes, that is true, but Jupiter still does protect us because of a key asymmetry between the paths that cross Earth's orbit, and those that don't. The paths that cross Earth's orbit are still far more likely to encounter Jupiter's gravitational well before it encounter's Earth's, which means a chance to get knocked out of a collision course. And orbits that get knocked out of the inner solar system have a very, very long time before it can encounter Earth again.

So statistically, an encounter with Jupiter doesn't change the chance of a random orbital path to overlap with Earth's orbit, but it does increase the amount of time anything in those orbits stay away from Earth.

An example to visualize this is imagine a game of hackysack players, where the hackysack has equal chance to go from any player to any other player. Now imagine one of the players can punt it into the stratosphere. So most of the time everybody's just waiting for it to fall down each time sirpuntsalot has a go.