Not entirely true. I have an LLC in New Mexico through a registered agent which does not disclose ownership.
EDIT: Elaborated
EDIT: Elaborated
No, you can just register as a foreign LLC [1]. Notably, you do not have to disclose ownership to do business as a foreign, i.e. non-Californian, entity in California.
[1] http://bpd.cdn.sos.ca.gov/llc/forms/llc-5.pdf
Disclaimer: I am not a lawyer. This is not legal advice.