There is a lot of nuance to this. You are not completely wrong. But you are definitely not right either.
Any resident of California who acquires the ownership of a firearm, and every person who becomes a resident of California and has firearms, has to register all these firearms. So if "you" in the above sentence means all current and prospective residents of California, and "need to register" means anytime a firearm changes hands or enters the state, then that statement is correct.
Anyone who reads your statement and concludes "California residents do NOT need to register all their firearms" is completely wrong. I know that this is not exactly the meaning of what you are writing, but it can be mis-interpreted as such.
There are some very interestingly complex grey areas. As everyone keeps pointing out, older firearms (handguns before ~1990, long guns before 2014) did not have their serial number on the DROS, or the DROS was not registered. However, the state DoJ has been going through old archives of DROS forms and other records (perhaps bound books, perhaps 4473 copies, I forget the details), and supposedly they have many importations into California and transfers, in many cases back to the 1920s. Now, that data is not a "register", because it can be incomplete. For example, while FFLs are required to keep all their records de-facto forever, and when they close down turn them over to the ATF, some such records are simply destroyed due to accidents; we've had gun stores burn down.
There are rare cases of firearms that can't be registered because they have no serial number. I think it was legal for manufacturers to build and sell guns without serial numbers up to the 60s or 70s. There are also the obvious mistakes in the processes that make the whole registry very slightly unreliable (like digits switched around).
In another generation or so, we will be able to safely assume that nearly all firearms in private ownership in California will also be registered. At that point, unregistered guns will be an exceedingly rare exception. How that will affect gun control law is an open question for the future.