I think the reason "access to code" and whatnot are mentioned is that it would be indicative that he wasn't fired but not told he was fired. If your client stops communicating all of a sudden it's often the case that you're not hired anymore and nobody there wants to tell you because that's never good news. And ultimately not telling someone and not paying them and not returning their calls will eventually let them figure out that they're fired. But in that case you'd definitely lose any kind of access that you once had. Passwords would be changed, your git privileges would be revoked, etc.

Prior to assuming that this person wants to blackmail them, think perhaps if there might be another reason it's mentioned.