At this stage of the game, I’d trust the professionalism of the Marines over the police when it comes to checkpoints.
That being said, I take a dim view of local police allowing Marines to observe a checkpoint. It’s fine line too easily crossed when it comes to Posse Comitatus and the military being directly involved with civilian law enforcement.
The cops say they invited the Marines. What I’d like to know is why the Marines didn’t invite the police on base to give them pointers when it comes to field sobriety tests?
It is easy to just get pointers, what they are probably observing is how people react at checkpoints. You can't just describe nonverbal queues and many you really can't fake. It is a term we use a lot called 'Educhaos', learning through the 'chaos' of real life. People react in unexpected ways that you can't put in a book or just describe, but you need to physically observe.
I can say from experience that MPs couldn’t arrest civilians even at the Pentagon. If attacked, they could noggin-knot them with nightsticks but not arrest them. US Marshals were there for that. This was in 1967.