I just bought a house in California, and you’re sort of both right.
For most homes sales, the current market value is the sales price, pretty much by definition. I’m sure the assessor’s office has a statistical model that says approximately what the house should be worth, and they’ll send someone out to investigate if the price is too far below what they expect, but all I got was a letter in the mail that said “sales price $x”, “current market value $x” (same x), with sections to fill out if the transfer is of a type that doesn’t trigger reassessment (it wasn’t).
In response to the OP, the least I would expect a house to go for would be the cost of the land minus the cost of demolishing the house and starting clean. There are certainly structures that you could put on land that will have a net negative effect on the total value, if they’re in bad enough shape that all you can do is tear them down and start over.