Its just another RL supporter who doesn't know the rules of the game they watch.
Your version is correct

Head and Feed to the team whos player catching the ball on the full with foot in touch

Unless he jumps from the field of play.

Agreed. But the OP was re: catching the ball on the full with your Foot in Touch. The same can be said for catching the ball with one foot dead in goal from the kick-off is seen as the ball going out on the full, or has that rule changed too?!!!

Should that not read, outside the field of play????

No. If he jumps from inside the field of play and over the touchline with the ball and then puts his foot/feet out it's head and feed to the kicking side.