Trained singers can use falsetto to sing higher without anyone hearing the voice is falsetto, especially using a microphone. There is a limit and you might just end up sounding like the Bee Gees.
The idea of falsetto is to not use excessive, unproductive tension and overblowing to play higher. It is an analogy that makes some sense, especially if you plan on “Stayin’ Alive” as a trumpet player.
So what does this have to do with you and playing brass?
Belt out the highest note you can sing. Then try to sing even higher; untrained singers tighten up, sing louder and strain their vocal cords.
Trumpet players do the same, instead of vocal cords we use lips and or the Valsalva maneuver. Some wrongly think that blowing harder, pressing the lips together and/or smashing the horn into your kisser will help develop a screaming upper register or any notes above the staff. BAD TECHNIQUE.
Thinking falsetto means you will relax and not use excessive force to get the notes out.
My suggestion is to stay with Greg, he is teaching the same idea and just not using the falsetto analogy to get there. It is the same path and same destination.
By the way, I have a reference for my writing. Bryan Davis, AirFlowMusic. He explains it on YouTube: https://www.youtube.com/watch?v=gUXeH5i1T7g and this is where I got my information.