Having been through the initial MSHA training and several annual updates I can tell you that the safety training is pretty simple.
The inspectors can find a violation ANYWHERE! Something as minor as a loose bolt on a railing is grounds for a citation and fine.
That being said, if you've been mining for 30 years it shouldn't be too difficult to follow enough of the rules to avoid being shut down. I didn't see the episode so am not sure what violations they had.
Dakota Fred should fall into the "glory hole".