I actually like the Hendrix-style of playing with the thumb over the fret to mute or play the low strings but if not used to it or new to it, it is a lot more difficult and painful to do, specially on a thinner neck with flatter radius.
Under foundation lesson, Tomo showed the way to hold the neck and bend strings similar to what your instructor said. Tom Quayle also mentioned something similar in youtube (called it "dead spider" position) when he was demonstrating legato technique. In my experience, after following the foundation lesson here, it did help improve the mobility of my left hand shifting up and down the neck because of less friction behind the neck as opposed to when my palm was pressed against the neck. The four digits (fingers) are also more relaxed because they don't have to curl as much, and I feel that my left hand muting is better in that position.
I still do use the thumb over the fret position when it calls for it, like when playing chord and melodic lines at the same time. And I see a lot of pros use both grips.
I think both grips are good techniques to learn and to have in your playing.
My 2 cents.