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The guy I learned to speedcube from was so good that we would secretly flip a corner or edge on his cube, challenge him to a race, and he would solve it to the point where only one piece was flipped, curse at us, fix it himself, and still beat us all by at least 10 seconds.

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Depending on his method, he probably saw the problem immediately when he got to the last layer.

Yep, it would be readily apparent by that point. You wouldn't even need to "solve" it first; you would see pretty much instantly that the last layer was in an impossible position.

Source: I got into speedcubing for a couple years in high school and averaged in the 30s, with a record of 26 seconds.

This is absolutely true. I believe he was at least using ZLL at that time, so it only took him 10-15 seconds to figure it out.

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