Punt "Plane"?

[TecnoGenius]

Where's the "plane" on a punt?

A few games back @ PAS there was a punt kicked by the opponent that landed outside the EZ.  It then rolled, untouched, so that (it appeared) the nose of the ball had broken the plane of the EZ.  But by "plane" I mean the plane that's used to tell if a TD has been scored: i.e. the inside edge of the goal line.

The ball did not go far enough to cross the outside edge of the goal line.  So it was on the line, but not actually into the non-line EZ area.

Our returner (Vaval) picked it up and returned it.  He was hoping it would roll into the EZ for a single, as he was waiting for it to roll farther.

My question is: did that ball "break the plane" and Vaval could have given up the single (what we wanted)?  Or, same question reworded: is the plane on a punt the same as the plane on a normal O play?

People around me were mixed.  Some said the plane changes on a punt to be the outside edge.  Some said the plane remains the same as a TD.

My guess is it did break the plane and Vaval should have downed it.  Why?  Because even if punting has a different plane than normal O (which I've never heard of but is possible), that should only take effect after the ball is touched and the returning team gains possession?

Bonus question: Vaval was chasing it, I think, having let it go over his head.  Does he have to get his butt into the EZ before touching the ball to be a single?  Or can he pick it up while he's outside the goal area as long as the ball is across the plane (whichever plane that may be)?