I think my intuition there stems from having a lot of full-stack responsibility (so the idea that it's someone else's problem was never a luxury I could afford, since it was always my problem) and having cleaned up a number of other people's very large spaghetti-code disasters.
The other possibility is that I have no special intuition into the problem (this is far more likely) but did have a fresh set of eyes, while all the people who were working on the problem were so intimately familiar with it that they couldn't see the forest for the trees.