Flat out + Overwatch

This came up in a game that I just played:

Can the passengers inside a vehicle that moved flat-out during the controllers turn, fire overwatch if assaulted in the following (opponent's) turn?

I moved a raider full of warriors flat-out in my turn. During the next turn, my opponent charged the raider. He said that I couldn't overwatch because moving flat-out prevents me from being able to shoot, and since I can't shoot (snap-fire or otherwise), then I can't overwatch. I argued that flat-out only affected shooting in my own turn, but since I couldn't find a solid ruling on the matter in the rulebook, I accepted his argument.

So, which is it?

Under fire points - the limit on shooting from flat out applies for the turn .... which the brb tells us means player turn unless it specifically says game turn.

It says turn - not game turn - so you can overwatch