I believe the wording says something to effect that the pitcher must enter a game where there's a chance he'll face the tying run to earn a save. So if a pitcher enters at the beginning of an inning with no outs, a 3-run lead is the most his team can have if he wants the save. For every out you remove, the number goes down one.
All of that's assuming that there's no one on base. If he would have entered with one out, one runner on, and a 3-run lead, that would have been a save situation because two batters could theoretically tie the game.