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First off, I don't get how the coin flipping analogy supports the notion of hot streaks. Tango read your comment and actually took it to mean you were arguing the opposite of your actual position. He thought you were pointing out how bad people are at recognizing randomness which might wrongly lead them to think if they flipped 7 heads in a row it meant they were doing something to influence the results. http://tangotiger.com/index.php/site/article/bill-james-on-looking-for-r...
Second, your final paragraph goes right past my head. Why would humans be expected to have LESS randomness than a robot in any circumstance? If humans were perfectly consistent in their performance (never hot or cold), I don't see how they could possibly have less variance than a Strato card. Pure randomness is the floor, so any thing that matches pure randomness must be purely random.
I have to agree with Tango here. When it comes to humans there is always some degree of skill involved so there is no point in asking if a particular skill exists or not. The question should always be how big the skill is. If that skill is so small that it is almost imperceptible, then it it isn't worth making a big deal about. You almost certainly won't be able to tell at any moment whether a particular string of outcomes is because of luck or skill based on results only (and claims of a player being "hot" are almost always focused on results, not anything the player is actually doing different).