It actually says somewhere that game belongs to the public, rather than to the owner of the land it lives on (unless you bred and raised the animal). So private land is not a free pass to do what you want.
However, there is also a reasonable expectation that a farmer, and possibly homeowner, can defend their crops/plants/land. I think farmers are actually allowed to do what they want - shoot deer, turkeys, etc that are damaging their crops, without a license. Homeowners can apply for a depredation permit, to exterminate wildlife that are destroying their plants. Though DFQ tends to concern themselves with larger game.
https://www.dfg.ca.gov/wildlife/hunting/bear/fgcode-4181.html
https://www.wildlife.ca.gov/Keep-Me-Wild/Wild-Turkey
https://www.dfg.ca.gov/wildlife/hunting/bear/depredation.html