I believe he means playing with the red part of the lips. Many players believe that we must roll our lips forward or in so that the red is hidden, at least when setting the embouchure. That works for some, although I believe what those players (who play well that way) are actually doing is letting the red part of their lips move forward in the cup of the mouthpiece and blowing a straight column of air into and through the mouthpiece and horn. Whereas what I believe Greg says in the video was that he realized he was rolling his lips in when setting the embouchure and when he blew air it was directed downward towards the ground (less efficient and effective) rather than more straight through the mouthpiece. My understanding is that Greg is recommending keeping things simple.
I have realized that I was doing the same thing Greg describes (blowing down towards my feet) and doing a weird pivot thing where I had to tilt the bell down the higher I played, eventually running out of top lip.
MTM has helped me realize that playing higher isn’t that much harder. I was clamping down the middle of my lips as I ascended rather than tightening the corners towards the aperture and blowing straight forward and arching my tongue, which I was doing.
I could never play much above the staff. G above the staff was the top of my effective range despite many years of practice and lessons from reputable teachers.
Now high C through E is relatively easy for me and I’m working on high F and double G.
And I’m understanding better how these apparently different opinions and advice about playing are actually closer together than they appear at first. The main difference I think is more about how to o communicate these concepts to students / players.
My understanding is that one main goal of MTM is offering more information for players to help those of us who couldn’t figure out how the trumpet works by reading/playing Clarke, Arban, Stamp, Schlossberg, Gordon, etc. Now I read those books and understand them better…for the first time. My $.02. Hope that helps until Greg responds.