It could be that it was perceived as a general conflict of interest. Maybe even be both ways; Tesla could be concerned that he's seemingly reviewing the product independently, without it being clear enough that he works for Tesla, akin to Amazon sellers reviewing their own products.
It's also possible that he was let go for reasons completely unrelated to the YouTube channel.
He didn't purchase FSD Beta, because it isn't for sale. Current FSD is for sale, and you will receive FSD Beta update when it gets out of beta. The only way to currently get FSD Beta is get selected (after applying) into the beta tester group for it.
If you want to record videos or reviews of yourself driving current FSD (that's for sale), you are more than welcome to, no one will stop you, and you aren't breaking any rules. FSD Beta is literally a beta tester program. And selective small-audience beta tests for all kinds of products typically carry extra restrictions in terms of what you can publicly reveal as a participant.
You just can't be an employee that violates your NDA by giving insider scoops.