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? ... People seemed somewhat attached to the anti-cheating heuristic.

The System 1 suspicion-detector would be less effective if System 2 could override it, since System 2 can be manipulated.

(Another possibility may be loss aversion, making any change unattractive that guarantees a different outcome without changing the expected value. (I see hugh already mentioned this.) A third, seemingly less likely, possibility is intuitive 'belief' in the agency of the cards, which is somehow being undesirably thwarted by changing the ritual.)