Yep, that’s the stuff- but it’s really thin. On the order of ‘I don’t want this to be seen in my skirt’ thin.
The very thick stuff used in head bands isn’t. And the ‘grippy’ part is just what you said- stuff to keep your head band from sliding down. I’ve found some that has waves, silicone, etc- but none has been thick on the order of 3 or 4mm. Mostly very thin, very light weight material.
I also figured there had to be a ‘stretch’ factor, like springs, but darn if I know where to look for it or what it’s called. 