To start, I don't know what the email said, nor do I have any certainty that it said something like "pull the paper". But equally, I don't have any certainty that it did not. I'm suggesting that without the email it is impossible to be sure either way. Given this unprovability, and given that Gelman is a brilliant statistician, I'm surprised that he's willing to make this a foundation of his argument --- unless he's talked personally with Wilkinson, or unless he's actually read the email.

1) The outcome. It's uncommon to remove a paper, but it happened. Senechal, explaining her decision to rescind, says "I have received concerned messages from several colleagues, warning of extremely strong reactions to the accepted version of your paper.... Their concerns include the very real possibility that right-wing media may pick this up and hype it internationally. There could be a massive fallout that may harm the magazine, the publisher, the editor(s) and, of course, the authors." Since we know that Wilkinson was one of the colleagues that wrote her, this makes me think that Senechal considered her a vote on the side of "do not publish".

2) In Wilkinson's Facebook messages, she says: "When I found out (a few weeks ago), I wrote to the editor-in-chief (Marjorie Senechal) complaining, as many others did, apparently. She ended up rescinding the acceptance (good, although why did she accept in the first place) and revealing my identity to the authors without my consent (bad). I received an obnoxious email from one of the authors, which is how I found out. No apology from the editor. Shabby." She is clearly happy that the acceptance was rescinded, and implies that this resolves her complaint (good). She does not mention that Senechal went above and beyond her suggestion of publishing with rebuttal.

3) Leland Wilkinson, in his email to Senechal (which he graciously allowed to be forwarded to Hill) says "I'm afraid I have to agree with Amie that a mathematical journal could risk harming its reputation by publishing an article like this." By contrast, when he says "if you do decide to go with this article plus commentaries", he does not attribute this to his daughter. I think this makes it likely that Amie Wilkinson's preference is that the article not be published at all, and that publishing with rebuttal would have been her second choice.

4) The lack of a clearly exonerating email. Wilkinson made a public response, but consciously chose not to release the actual contents of her email. If the email made her look good, I think should would have produced it by now. I don't mean this as a personal attack on her integrity, just an observation about common human behavior. I thought most of the people in the released email chains came off looking quite professional. The conspicuous absence of this email makes me want to see how it compares, and see whether it matches Wilkinson's self-description.

Based on my reading, no one who has seen the email has described it as such.

Other than Wilkinson and Senechal, does any one else claim to have seen this email? The only description I have seen from Senechal is that the emails (as a group) "concerned not the substance of your article but the very real possibility of extremely damaging fallout", without any specific commentary on Wilkinson's email. I think everyone else is relying on Wilkinson's summary of what it said, rather than the email itself.

If I can turn the question around, what makes you confident (if indeed you are) that Senechal could not have interpreted Wilkinson's email as a request that the paper should not be published?

edit: I should probably add that I have no particular problem with Wilkinson (or others) lobbying an editor to rescind acceptance of a paper that they feel is harmful. In this case, I think it's better to publish and discuss, but people should act their conscience. But I would be bothered if Wilkinson was shown to be privately lobbying against publication while publicly claiming to have advocated only for publishing with rebuttal.