Whilst seeing an a/c rolling towards you would be a nasty moment, an ambulance can brake or speed up considerably faster than the a/c. The vehicle driver could have decided to stop, or accelerate across the runway with the same mental speed as they make when approaching an intersection with red lights.
Even when crossing green lights - when running under blues and siren - you have to expect that someone will not see/hear you and approach you from your blind side. For example, if they are jumping a light towards your intended path. This is all part of the Day 1 training, so (as the situation is reported here) I have my doubts as a runway intersection has considerably better sight lines than when entering (say, Hyde Park Corner or Marble Arch in London - both junctions have 5 roads of double lanes, meeting around a large circle with a lump of stone in the middle to block your view.
When there is one taxiway and one runway and two vehicles and no visual obstruction? (A nephew of mine has been driving amublances under blue lights for four years.)