Legal Question in Real Estate Law in California

Technically, yes; but if you didn't know and had no reason to know, while the neighbor did know all along that damage was being caused and didn't tell you, this might be enough for a judge to find an "estoppel." When someone is partially to blame for their own harm, and have not done what they equitably should have done to mitigate damages, a court can hold that the plaintiff is estopped (prevented, equitably barred) for asserting a claim or recovering all damages. My suggestion is to offer to remove the tree at your expense if the neighbor will repair the damage at his expense.