I checked it because it didn't feel true, and news reports were all over the place, so I hunted up the state police release. The police were on the domestic abuse call on one side of the freeway when Giuliani went by on the other side as a passenger. Maybe they were rubber-necking and slowed down.
Sounds like a way to get his name in the good graces of the press? Maybe they have a police scanner they listen to? Weirder things have happened, but this is Giuliani....
It crossed my mind that they heard the troopers talking about the domestic incident at the scene after crashing, but I like your idea of a police scanner, many people have them. I suppose they MIGHT have been flagged down, called police, then made a U-turn at the next I-93 overpass but... I dunno.