Sorry, but that is factually incorrect.
"licensed gun owner to open-carry in California", as I read it, is "a gun owner licensed to open-carry in California".
Regardless, you can't get a license to open carry in California, as no such license exists, and open carry is illegal in California under California Penal Code Section 26350[1]. So, you may be able to legally carry a firearm in California, but unless you're a law enforcement, you may not carry openly. This has been adjudicated in court in Peruta v. San Diego[2], and the courts found that an outright ban on open carry for the citizenry comported with the second amendment.
So, as a private citizen, you might be able to carry a firearm, but you would have to do so in a concealed fashion, and only after being licensed to do so. In order to obtain a license, you have to apply with your county sheriff, they have to evaluate whether you are of good moral character, whether you have a legitimate reason for carrying a firearm, that you have completed 16+ hours of training, and that you are a resident of their county. Noting that 'self defense' is not a valid reason for issuance, most applications are denied, though that undoubtedly varies from county to county.
[1] - http://leginfo.legislature.ca.gov/faces/codes_displaySection...
[2] - https://www.ca9.uscourts.gov/content/view.php?pk_id=00000007...