Certainly a case for both parties to have yielded in this situation. Just taking Gaz's presence out of the discussion for a moment, looking at the footage, the mini-bus driver does appear to be travelling faster than the road conditions (i.e narrow road, parked cars, residential area etc) should have dictated. Given that the driver was carrying students, he should have been driving with a modicum of caution and certainly both hands on the wheel.
Difficult to pinpoint where Gaz could've pulled in from the footage (though he concedes it was possible); the mini-bus was visible from quite early on and so presumably the driver had equally as good a view of what was coming towards him? All boils down to hazard perception again. Both parties could have anticipated the potential hazard before them and taken some precautionary action; the difference is the vehicle could've caused untold damage both to Gaz and possibly the students travelling in the vehicle.
Maybe the sun impaired the driver's vision; maybe the kiddiewinkies were causing a distraction (I've been there

); maybe the driver miscalculated his manoeuvre and then panicked. Alternatively as asserted already maybe they were guilty of boorish driving. Whatever, it's not a safe situation, and certainly something the school should be addressing.