On the surface that is true, but behind the first responders are the second responders.
It was under Bush that the US Northern Command was established(by proclamation) and you need to know what their duties are. DHS was created (by Congress) and these DHS grants to local law enforcement are substantial.
The War on Drugs began with Nixon and Reagan was the first to give military surplus to local law enforcement.
There is lots written on this subject but Balko's book, "Rise of the Warrior Cop", published earlier this year is the most comprehensive
“”The US military cannot be used for enforcement of civil order” “
____________________________________________________
It is usually the state’s national guard that is called up
when there is civil disobedience that is too much for local police. I remember it in Memphis.