Please understand that cops are NOT great resources on the law. Even one fresh out of the academy. They're better resources than nothing, or than "word on the street," but they are not lawyers or D.A.s They are trained in a classroom and by training officers on the law, and their instructors and training officers are also not lawyers or D.A.s.
Cops did not take the job because they wanted to learn about the law, or because they were good at reading statutes and interpreting court cases. They became cops because they wanted a good career, wanted to help people, and wanted to fight crime (plus a few who want to be cowboys).
Cops can give you a very good idea of what they'll arrest you for. This is useful information. But the end result of the encounter will depend on whether you actually violated the law, which will depend on you, your lawyer if you need one, and the D.A. The end result depends on the law itself.
Nowhere in California law is a double-edged blade mentioned. You should treat them as any other knife with a single-edged blade. But keep in mind that a cop--just as he told you--will be more likely to arrest you for a double-edged blade because they *believe* they're illegal. They might let you go if you have a 5" single-edged folder, but hook and book you because you have a 2" double-edged blade. Add this to your knowledge before carrying your double-edged blade. But arm yourself with a thorough knowledge of the Penal Code and any court cases that interpret the relevant statutes. The law librarian at a county law library (located in big courthouses) or at your local law school can help you find the "annotated codes" that will be your starting point.
Edited to add: There are exceptions to the above. But they typically won't be a rookie cop. They'll be a cop who's in a leadership position who also happens to be an intelligent, well-read type of person who knows his or her stuff. Just like you probably won't get expert ballistics info from a rookie cop, but there are cops in the department that know a hell of a lot about ballistics if you know where to find them. A friend of mine is an LAPD sergeant and knows the weapons laws as well as any lawyer. But several times he has had to explain to his officers who've arrested someone for "carrying a concealed dirk or dagger" that a locking, one-hand opening folder that's completely concealed (this part relates to local laws) is legal, despite his officers' being 100% convinced they had a felony arrest.