Whats the ruleing on this?

[Mojo Tooth]

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If you shuffle again, the outcome has been changed.

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So what? It's still an unknown outcome. This is exactly my point. ANY unknown outcome is just as legitimate as any other. I wouldn't mind if, instead of burning a card, the dealer shuffled the deck before dealing the flop, turn and river. Of course that's impractical for reasons of speed, but completely equivalent.

What if you found out that an online site didn't bother to actually shuffle the deck before dealing a card off of it? It would be exactly mathematically equivalent to simply choose a random number between 0 and 51, deal that card, then eliminate it from the deck. Then for your next card, pick another random number between 0 and 50, deal that card, so on and so forth.

By your line of thinking there would be no pre-determined outcome, so it would be somehow undesirable, yes? But you would never know the difference because it's EXACTLY THE SAME.