First of all, California allegedly does not have a mandatory registration statute for all firearms. Guns like those belonging to your friend who purchased them long before gun laws became draconian do not need to be registered.
There is a catch, however. If you intend to carry the gun or you are charged with illegally carrying the gun, and it is not registered to you, it can be charged as a felony.
The Voluntary Registration form is one way to register your gun with the California DOJ. Once you do that, the information will be entered into a CA-DOJ database where it will remain until some paperwork later says it was transferred to another party.
In California, transfer of a firearm (or a loan of a handgun over 30 days) between two persons without going through an FFL is illegal. Even C&R handguns must be processed through an FFL.
If your friend is worried about the gun being traced to him, it's doubtful that it would happen. Given the freedom with which guns were sold between 1955 and 2001 when personal transfers were required to be documented, it is possible that the gun could have legally changed hands dozens of times without a record.
I'm also reluctant to give the "gubmint" any information they don't need to know. But depending on your personal circumstances (age, length of time in CA, gun type, etc.) it may be better to voluntarily register the gun.