You can't deploy military assets against the population. It's illegal, since that's how coupes happen. That's why we have the National Guard. Read up on Posse Comitatus. So, it doesn't matter that the Navy is in town.
Oh come on. An armored vehicle loned to the local police in a case of a school shooting is going to undermine the goverment?
Sadly your use of the word government is so sickeningly far from the meaning of a constitutional republic, I weep that yes such things do undermine the government (IE the people of the united states of america and not a small military cabal of police beholden certainly not to its local citizens).