Texas is the sole exception to this rule, at least when it comes to laws (but there's a separate question of how laws are enforced in other states... in some places, the sheriffs might look the other way in practice, and it's easy to fudge). It has nothing to do with stand-your-ground.

SYG by itself only removes the duty to retreat in the face of danger if you can. It does not allow to use lethal force when you're not in danger, merely to prevent a commission of a crime.