I don't know precisely how US hot water tanks deal with that problem, but I'd bet that there is more space in the tank beyond the point where the tank will shut off incoming cold water.
Looking at our hot water tank, it seems like it's dealt with in the same way as in the UK -- minus the cold water tank. That is, there's an open pipe running down the side of the tank (so that the hot water that vents from the top doesn't spray someone in the face). Any water released in the process will make a puddle on the garage floor.
I'm assuming though, that, like you suggest, there's extra space in the tank to accommodate fluctuations without the need to constantly spill out the pressure release, and the vent pipe is just a safety release.