For California, that is wrong. You can claim right away if you are fired. The employer can dispute it however they have to prove they tried to rectify the situation. The way the system works, the former employee has to dispute the unemployment rejection if the employer wants to try to claim it was a valid firing. So if you do get fired and there was not a pattern of behavior or something that you were warned about, then you simply appeal, state your case and the judge will almost certainly reject the employers false claim.

Unfortunately, I know this by experience. I was fired for some fishy business and it was obvious at the hearing. So always file for unemployment unless you are certain it will not be granted. Unemployment also qualifies you for health insurance through Covered California.