That's not what bill1952 was talking about. His original quote was: "Not to mention that sub is not just "sitting" on the bottom. It is being pressed down into it by untold pressure."
He's confusing pressure with weight. The pressure on the sub is equal all the way around, regardless of whether it's surrounded by water, on a rocky bottom, or stuck in the mud.
It works just like a suction cup on the wall. It stays there because of air pressure on the outside. To you move it you have to equalize that pressure by getting air under it.
This is an entirely different thing, and is more akin to the pressure differences between that inside the sub and outside. In your cup on the wall, you've sucked the air out creating a (partial) vacuum. That force pulls the cup into the wall, but the wall pushes back with equal force. The friction between the cup and wall (created by the vacuum) are what hold the cup in place. You could then cut the wall out around the suction cup and create a little "atmospheric submarine." Set it on the floor and pick it up. It won't be any harder at sea level than it would be in Denver, even though it would be missing a full mile of the thickest atmosphere above it in Denver.