P.S. I think you have thought about this well and your comments are interesting and insightful, but I think you are just missing one important piece of what I originally said
I'm convinced you don't understand my argument and example. You are ignoring that the pressure that the people are exerting on the ground must be accounted for in a real-world scenario where a submarine's hulls don't stand on the ground. But I'm having a hard time following you much of the time. Is English your first language? For example, just looking at your first sentence: "My point is that that inner container has one less atm of pressure relative to the water outside than the inside of the sub itself, but neither sees any difference." Aww it makes my brain hurt!
And how much load must the foundation, or the ground carry? Do you actually think that it is anything less than the "pressure" (the weight in this case) of the entire building? To be really pedantic, I did not assume that the inner layer must carry the entire load, I argued that. And storeys is spelled stories. Pressurised is spelled pressurized.
Anything that is not part of the structural integrity of the submarine is exactly that--it doesn't have anything to do with the submarine hull and it's ability to withstand pressure. In other words, it doesn't appear to have anything to do with what we're talking about. Where you are going with this?
I don't understand your comment -- It seems confused to me, perhaps you could explain it? I don't know where the "really flexible hulls" assumption comes from. Could you explain this, I have no idea how it might relate to my explanation? Are you referring to "springs?" As I said earlier, it doesn't matter if the intermediate pressurizing occurs with something flexible like springs, or inflexible like water. The rest of your comment appears to be very confused. First, if there was a vacuum chamber inside a sub, the pressure inside the sub would not be the same--There is now a vacuum inside the sub! That means that the pressure would be 0, which would be an unsurvivable change for any human occupants that might have been in there. Second, your second to last sentence is quite amusing. You are saying that because the pressure on the inside is the same, the pressure on the outside stays the same? Do you really think this is logical? Do you think that if you blow up a balloon, take it 1000ft deep, it will have the same pressure on the inside? Do you think it will be the same size?
That idea won't work because it doesn't actually make sense. While it is definitely an interesting question; and one that I was initially puzzled by, I think you will be surprised by how clumsy the intuitive logic that brings us to that conclusion is. Consider your onion, with two layers, and you are standing between them. To make things simpler, lets assume that instead of water pressure you actually have pressure from weights, and lets also change your onion from spherically shaped shells to just two flat surfaces. For example, you could imagine that you are just standing on an imaginary, levitating sheet of plywood and there is a sheet of plywood above you. The "water pressure" from above you is say 100 lbs. This is how many weights are on the sheet of plywood above you, and it is as much as you can hold. So you say, lets "pressurize" the intermediate onion layer (you), and you position springs on both sides of you (or you could use water pressure). With this new pressurized layer, you can now withstand twice as much "water pressure" from above you, for a total of 200lbs. But that has nothing to do with how much pressure is being exerted on this imaginary sheet of plywood beneath you. As you see, you could build a million onion shells and it wouldn't change anything about how much pressure the inner most layer, or the bottom sheet of plywood, must withstand. Indeed, all submarines already use your multiple hull theory, but not in the way you imagine. They all must withstand the pressure from a layer of ocean above them AND a layer of atmosphere above the ocean--the ocean doesn't protect against the atmospheric pressure.