Yes, the story Grimm told here didn't quite fit with what we'd already heard in book one, but that could be either Grimm lying to Abby or Jim changing things.
I just read some paragraph of the two books and I've noticed a few things besides Rook (that I bet Grimm purposely left out of the story, even when it means lying to Abigail).
1) In TOA Grimm said Alex was a midshipman. In TAW Gwen said that for what she found, the three of them were lieutenants. It could be easily explained by Gwen being confused or by the fleet lying to justify giving the promotions to Rook and Bayard (to smooth things with them). Nevertheless, there is something weird. In the same TOA Grimm said that he "had seniority on Alex and he was on shambles. So I assumed command." but if Grimm was a lieutenant and Bayard a midshipman, it was obvious that Grimm had the command, no need to mention Alex being in shambles or anything. So I think what happened is that Alex began the journey as a midshipman and was promoted to lieutenant in the trip itself. But it is not clear.
2) in TOA Grimm said he cut the XO throat and dropped him by the side. In TAW apparently the XO had been beaten to a coma. No possible explanation but someone lying (perhaps the Fleet).
3) What I see as more serious, because there is no politics or Fleet involved. In TOA Grimm said that the men, especially Kettle, supported him. In TAW Kettle told Gwen that he did not know Grimm when he was on the fleet. So...What the Hell? No Beta caught that? Will be relevant for the future?
More important, in TOA Grimm said that