It depends on how supply is increased. If you allow single-unit housing stock to be converted to multi-unit, that causes existing homes to rise in price as you say. But rezoning industrial buildings to high-density residential causes existing homes to drop in price. I believe the solution in SF will mostly be the latter, such as converting warehouses in the Mission into lofts.
Also, California's weird laws mean that property taxes don't go up much even when the value of houses rise a lot.
So most NIMBY homeowners are genuinely defending against property values dropping.
It's people who own houses that are YIMBYs, because removing zoning restrictions causes land value to go up. It's people who live in them who are NIMBYs, because they fear density in their neighborhoods will lower their quality of life, and that they will eventually be forced to sell due to a rise in property taxes as a result of their property values rising.
If they're old, that's a scary proposition. If they're young enough that they have kids in the public schools, they're probably young enough that they won't have a problem selling their home for a boatload of profit and moving to another exclusive neighborhood.