Yes, a theoretical future AI that would be able to self-correct would eventually become more powerful than humans, especially if you could give it ways to run magnitudes more self-correcting mechanisms at the same time. But it would still be making ever so small assumptions when there is a gap in the information it has.
It could be humble enough to admit it doesn't know, but it can still be mistaken and think it has the right answer when it doesn't. It would feel neigh omniscient, but it would never truly be.
A roundtrip around the globe on glass fibre takes hundreds of milliseconds, so even if it has the truth on some matter, there's no guarantee that didn't change in the milliseconds it needed to become aware that the truth has changed. True omniscience simply cannot exists since information (and in turn the truth encoded by that information) also propagates at the speed of light.
a big mistake you are making here is stating that it must be fed information that it knows to be true, this is not inherently true. You can train a model on all of the wrong things to do, as long it has the capability to understand this, it shouldn’t be a problem.
The dataset that encodes all wrong things would be infinite in size, and constantly change. It can theoretically exist, but realistically it will never happen. And if it would be incomplete it has to make assumptions at some point based on the incomplete data it has, which would open it up to being wrong, which we would call a hallucination.