From the numbers I can find, I don't think this is true. The biggest population constraint in the Valley by far comes in the form of explicit density constraint

From the numbers I can find, I don't think this is true. The biggest population constraint in the Valley by far comes in the form of explicit density constraints, such as minimum lot sizes, not rent control. Palo Alto has no rent control, for example, but is less dense than SF, despite the fact that demand exists for much denser housing to be built (especially near Stanford) if it were permitted. Some kind of scared-rich-person-club mentality going on where they're worried that allowing apartments, or even townhomes, might bring in too much riff-raff, so by law everything has to be an undivided and large single-family home (in a large portion of the total area).