I don't know how to respond to this. I feel like I have addressed all of these points elsewhere in the comments.

A summary:

• The poker game is an example. There are more examples involving things with less obvious rules.
• My reputation matters in the sense that they know wasn't trying to cheat. As such, when pestered for an answer they are not secretly thinking, "Cheater." This should imply that they are avoiding the cheater-heuristic or are unaware that they are using the cheater-heuristic.
• I confronted my friends and asked for a reasonable answer. Heuristics were not offered. No one complained about broken rules or cheating. They complained that they were not going to get their card.

It seems to be a problem with ownership. If this sense of ownership is based on a heuristic meant to detect cheaters or suspicious situations... okay, I can buy that. But why would someone who knows all of the probabilities involved refuse to admit that cutting the deck doesn't matter? Pride?

One more thing of note: They argued against the abstract scenario. This scenario assumed no cheating and no funny business. They still thought it mattered.

Personally, I think this is a larger issue than catching cheaters. People seemed somewhat attached to the anti-cheating heuristic. Would it be worth me typing up an addendum addressing that point in full?