You guys all talk about not putting pressure with Thumb. What does that even mean ??

The idea is that only a very small pressure is needed from the fingers to put the string in contact with the fret and form a note. If you put more than that your note with get sharp and you uselessly tire yourself.
So yeah basically you should be able to fret without using your thumb, even if it's more convenient to use it.

 

With a quality strap set to the correct height and a well weighted bass, neck dive becomes less of an issue. With a proper setup and low action (strings close to the fretboard), you should be able to fret the strings without pushing the neck back too far.

I try to gently rest my thumb on the neck so I can quickly move it about with minimal resistance. I used to squeeze the buggery out of it which really affected my ability to play cleanly and comfortably.

I think thats what people mean when they say don't press, since press is commensurate to pressure on the neck.

Hope that makes some sense.

 

Here is the thing with the left thumb is you don't press harder than you have to, but when you're moving your hand from one position to the next you completely relax the grip so there is no pressure and your thumb is just gliding.