I sure hope I didn’t come across on the pro-bungee-vacuum side of this discussion 
The “vacuum airship” is completely different, though. In a regular airship, you have equal pressure of about 1atm on both sides of a semi-rigid membrane, and changing one side of the membrane to a vacuum is obviously a drastic change in the pressure differential, requiring a fully rigid membrane that would be way too heavy to be supported by the buoyancy of the air displaced.
But water is 1000 times denser than air. So what’s relevant in a sub is:
(a) buoyancy, and the difference between an air space and vacuum space is only 0.1% of the density of the water being displaced, so adding an evacuated space is no different than making the air-filled space of the sub a bit bigger;
(b) a hull that is already designed to withstand a pressure difference of >25 atm, so increasing the requirement by 1 atm is not a huge change.