So, the statute is different from what’s on the DMV site. Essentially, you have to register your car if you are a resident. There are various things that create either evidence or a rebuttable presumption that you are a resident–but typically a full-time student who is a resident of another state would not be considered a state resident unless he or she takes steps to become a resident. So I feel fairly comfortable in saying that my daughter would not be required to register the car until she takes steps to become a permanent resident of California.
But it still might make sense from a hassle point of view to register the car there if she’s going to get tickets that she’d have to fight, etc.