This is a follow-up to this question: Should I recommend rejection for a paper I referee if the authors don't make changes that they could have made?
To recap: I was sent a paper to referee by a top journal. My first report pointed out that the authors had only considered one of two possible behavior patterns that their system might have. When the authors resubmitted, they basically ignored what I had said (although see below). So I sent it back, asking that the changes I had asked for before actually be made.
When I read the second draft very carefully, I saw they had actually added a very short paragraph that seemed to be arguing against the second type of behavior I was worried about being possible. It was so minor I didn't even notice it before I asked my earlier StackExchange question. However, the manuscript authors made an error in their attempt to demonstrate this point quantitatively; as I pointed out in my second report, their argument actually showed that I was correct.
Now, they have submitted the paper a third time. This time, they very enthusiastically acknowledge that I am right--both types of system behavior are expected to occur. However, they now claim that their numerical calculations actually include both possibilities, and that they actually did all along! The letter says that they just explained things really badly.
They have made more changes to the manuscript. It now states that both behaviors can occur and that both are fully included. I am not in a position to check whether their results are consistent with this. The paper does a lot of heavy numerical calculation, which would take a long time to replicate. Since the bottom line result is not going to depend much on the intermediate details, it is plausible that their graphs could have been showing the fully correct answers all along.
However, the format of the paper suggests otherwise. Add to that the fact that the second draft of the paper actually argued obliquely against the type of behavior that they now admit is natural. I feel like there are two likely possibilities. The first is that the authors are being dishonest. They missed the second possibility, and now that I have pointed out that it definitely occurs, they have reasoned that they can fib about the matter and it will be difficult to refute their claim. I am rather unhappy about this possibility; I hope it's not the case. The second possibility is that the communication between the two authors of the paper was extremely poor. The person who did the actual writing would have to have been quite ignorant of what his coauthor was actually calculating. This is a less troubling but still far from ideal situation.
So, once again, I find myself unsure what to do. Should I share my misgivings with the editor? Or should I take the current draft's claims as is--chalk the whole thing up to incompetence rather than dishonesty? I have, after all, no concrete evidence of fraud.