Not sure about California. Here in Las Vegas (and I'm told this is a national law), if your property is sold at the trustee sale to an investor, the investor also has to honor your lease. However, if the property is sold to someone who intends to owner occupy, you only have 30 days. Sometimes the new owner will negotiate with you and offer you cash for keys to move, but they're not obligated to.
If the property is sold to a 3rd party at the trustee sale, the bank isn't taking it back at all. They are agreeing to sell it for a minimum amount at the trustee sale. So no, I don't believe that's correct.
The way i feel is , if it was me, i wouldnt want to stay in a place with this hanging over me, knowing i would have to leave 1 day, so instead of losing another nights sleep, i would accpet a payout to be able to move on and be secure in where i was living.