No. The timing being off could and often does keep the engine from running or running properly if you can get it cranked, but it wouldn't stop your cams from moving.
The timing belt is like any other belt on the car, they break sometimes. In this case one of your cam gears could be a little off-center or a little loose causing excessive belt wear, could be the same type of problem down on the crank. Or the belt could just have been old and tired and decided that since you were already at a red light it was time to call it a day.
Since the timing belt is what links your crank to your cam's, when it goes there's literally nothing there to control the rotation of your cams.
Edit: So let me make sure what the situation is... the belt appears to be intact, but the cam gears aren't rotating when the engine is turned over?
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