You're right of course, you can shoot home invaders except in the Northeastern states where they're protected. Shootouts with the SWAT Ninjawarriors aren't usually real productive without sufficient backup. They'll kill you, your family, your pets and burn your house, then they'll tell the story any way they want to.
Yup.
It was a retired copper who told me very clearly: 'there's only one story if the other guy is dead.'