A little thing called the Posse Comitatus Act?
You know, the one that says very damned specifically that the military cannot be used to enforce domestic civil law?
So, the question is begged:
Why would they have a need to train with a civilian police Special Weapons and Assholes Team?
Oh, okay. So they are supposed to go train in urban areas in the middle east?
SWAT specializes in urban tactics. Special Forces may need to know that for deployments over seas. Special Forces are usually patriotic, I highly doubt they would go along with deploying in the states.