I didn’t watch the whole video, so I didn’t hear Justin say that, but if you watch his hand position, he certainly isn’t playing with this thumb behind the neck. He generally plays with his thumb visible above the neck. In fact, when he demonstrates the wrong way to play (at around 0:45 of the video), he drops his thumb behind the neck. Try to position your hand the way Justin has it.
I would say that if you angle your fingers correctly, it’s not that stretchy. Again, he talks about finger angle at 0:45 of the video. If you don’t angle the fingers, it is indeed stretchy (which Justin mentions).
That’s not to say that it’s easy! Getting enough curl in your fingers to not mute the other strings takes experimentation and practice.
One other tip: make sure your nails are cut short, especially on the index finger. If I have even the smallest nail protruding, I can’t get the tip of my index finger straight enough to prevent the high-E string getting muted.
Good luck!