His first and second points are roughly correct. His mistake is in his third point.

Relativity does say that all frames of reference are equally valid. But this doesn't mean you should pick one and prefer it over others. In fact what it says is that there is never any reason to prefer one frame of reference over another except that it simplifies the problem in front of you.

The jump to the earth being motionless is a pure act of faith, with no scientific backing.

Jay