This is incorrect, it's about fuel. By the time the rocket has completed first stage separation it's traveled a long way "horizontally" and is no longer near th

This is incorrect, it's about fuel. By the time the rocket has completed first stage separation it's traveled a long way "horizontally" and is no longer near the launch site. They are trying to create a landing spot as close to the rocket as possible so it can't make it back. The only orbits that can reasonable get all the way back to land are fairly low and from specific launch sites.