It's subtle, because some of the impossibility proofs are effectively saying that any real proof needs to be somehow sensitive to whether it's in an imaginary universe with oracles, so they can _fail_ in them!
It really is mind-bending stuff -- I have only the vaguest idea of how these proofs could work, but you summarized it beautifully.
As an aside, this is also perhaps also one of the best motivating examples of the idea of "oracles" in math. ("Ok, assume we can do $IMPOSSIBLE_THING... now what?" :) )
As an aside, this is also perhaps also one of the best motivating examples of the idea of "oracles" in math. ("Ok, assume we can do $IMPOSSIBLE_THING... now what?" :) )