One more datapoint: between 2013 and 2014 the net change in population in the bay area was 100k, we can assume things are more or less the same as before meaning that H1B immigration counts for ~50% of the total change. If you can find more recent numbers (took me 30 seconds to find the links I added) then we can redo the math and see if there's major problems with my statements, but I really don't see how that could be the case.

https://ww2.kqed.org/news/2015/03/26/youre-not-crazy-the-bay...