I believe they did a follow-up study to try to adjust for this. In the follow-up they were able to surreptitiously note the results of the coin flip (without the flipper knowing). The people who flipped the coin but ignored the result because it didn’t go the way they wanted still rated themselves more fair than those who did not flip the coin but just decided to make things go their way without going through a coin-flipping ritual first.
I believe they did a follow-up study to try to adjust for this. In the follow-up they were able to surreptitiously note the results of the coin flip (without the flipper knowing). The people who flipped the coin but ignored the result because it didn’t go the way they wanted still rated themselves more fair than those who did not flip the coin but just decided to make things go their way without going through a coin-flipping ritual first.