It is the typically the license plate that controls. From the license plate the registered owner is contacted. Of course, if the license plate and registered vehicle do not match (in the case of a stolen plate) the ticket is invalid. You still must take steps to fight it.
Considering that LA District Attorney Carmen Trutanich has created a new policy cracking down on ticketing officers who don't have independent recollection of moving violations, it's very, very unlikely that this parking ticket wouldn't be enforceable for this reason, but you could try to contest the ticket based on this if you want to at least buy yourself some time.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.