What I find the most surprising in this story, without having to take sides about the merits of any of the discussed papers, is that the initial refutation of the work of Bellgrau et al. was reviewed by Bellgrau et al.
If this fact is true, then there is a clear conflict of interest: Bellgrau et al. should have declared it and declined to review, or, barring this, the editors should have noticed it and ignored the review.
If a paper is being contradicted by another, it's quite common to send a copy for review to the original authors. Who better to look for holes in a new paper than someone who's expert in the field and about to have a big problem on their hands?
The editors are the ones who make the go/no-go decision. In my field, I've seen papers that are faulty and have been rejected by experts be accepted by major journals. There's a lot that goes into the go/no-go decision by an editor; I don't envy that job.
If the article is correct, then the editors at Nature may have made the wrong decision. Most of us are sufficiently un-expert in the field to make any conclusion.
I believe in this case, where two outside reviewers recommended acceptance and the original authors recommended rejection, that the appropriate action for the editors was to get the two outsider reviewer's opinion on the original author's report. Even better, a third outside reviewer should be contacted to assess the original author's report.
I'd even call for greater numbers of referees. There are big practical problems with doing so, but the uncertainty associated with the traditional two or three referees is >50% ( sqrt(3)/3 ). An ensemble of 7-8 referees may produce a more reliable result.
Bellgrau deserves the right to know that there was a challenge to his paper, even to answer questions raised in the refutation, but it should all be done in the open after some point.
If this fact is true, then there is a clear conflict of interest: Bellgrau et al. should have declared it and declined to review, or, barring this, the editors should have noticed it and ignored the review.