Yeah, he is in probationary period but if he get fired does he get a permanent bad record in his EMS career?
I see you're in California. I can say that in Maryland, the answer to your question would be
No. The state-wide EMS oversight agency maintains records of which EMS organizations a person has been affiliated with, but the record, to my knowledge, does not include information on why affiliations are discontinued. In other words, the record does not say why a person is fired, or even that they're fired at all; it just says that they're no longer affiliated with that organization, whether it's a municipal or volunteer fire department or company, a private ambulance service, or some other business.
I haven't paid much attention to news regarding EMS in CA, but I understand that right now, a state-wide EMS personnel tracking system is being implemented. Whether that system will include specifics, such as what a person is fired for, or whether it's just going to track basic info such as MD's system, I don't know. JPINFV seems pretty knowledgable about CA EMS law, and can probably provide more info about that.
Keep in mind, though, that although there may be no bad record in an EMS database somewhere, the previous employer will maintain that information for a few years. If your friend applies for a position with another company, and lists the previous employer, and the new company contacts the old company, they may find out about it. That may make it sound as if your friend shouldn't list the former employer on an application, but that is a Bad Idea. Background checks are routine for EMS employers, and a simple check with the Social Security Administration will reveal his former employment, so if it isn't mentioned on the application, that's automatic grounds for the application to be rejected. Now, the previous employer, if actually contacted, really shouldn't say anything more than, "No we would not hire that person again."
Your friend's best bet is to be truthful on his next round of applications, and explain why he was fired. He should try to find some way to make it sound as un-negative as possible, of course. Whatever the specific reason was, he should say that he now knows the right way to do it, and that he understands why it's important, etc.