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Unabridged: Yes indeed. However, your scenario is actually more complicated than necessary. A site can shuffle quite honestly (using all the best hardware random noise type rng systems available) and pass every statistical test known and still cheat by doing nothing more than sending a single message to prop players notifying them that they have a guaranteed river win. A smart prop player can then creatively control when they win and lose even to the point of redistributing funds from winners to losers.

It takes about 2 lines of source code to do what I just described and very little bandwidth.

Maybe the OP can chime in here and verify the ease with which this is possible.

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Downside: Prop then documents the process and threatens to post it all on 2 + 2 if the site doesn't pay them a million dollars.

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Yes indeed. The scenario is sound only if the prop has as much to lose as the site does. The prop player can of course be nothing other than a site operated bot.