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I doubt this is something the average person can do. In my experience, most people can recognize a scale as being major or minor; people with some music background can tell you the relative major to a minor scale or vice versa; and people with a bit more music background may be able to spit out the seven church modes. Independently you've got the talented folks with perfect pitch (play a random note and they can tell you what note it is) and relative pitch (play a few notes in a melody or sequence and they can tell you what notes they are).

What you're describing I think is far beyond the layperson's ability. I think it's something one can learn if he is interested, but I don't think this is something that most people inherently have. Sounds like the Redditor had a conceited professor who sincerely couldn't understand why not everyone was as great as he.

Either that, or I'm just ashamed that after eighteen years of music I still can't do this in my head.