*Thank you all for your comments. The fact remains that Demurger does mention (two times) that Bohemond was present with his troops at Baghdad, and publishes the info in two very reputable books. In a subject where we precisely speak about relations between Franks and Mongols, it is worth mentionning. If you wish we could even isolate Demurger further "Demurger makes a unique and unreferenced claim that Bohemond and his troops were in Baghdad", but I'm very reluctant to condone "book-burning" ("he's wrong, it never happened, don't even allow it to be mentionned"). Demurger being an extremely serious historian, I'm sure he actually has some info to back up such a claim. Furthermore, all the rationale against his claim is actually original research based on the analysis of a possible schedule conflict: I'd like to see at least a published source saying that Bohemond was not in Baghdad, or that Demurger is wrong on this count.  
 *By the way, several of the editors here have stated that Antiochian troops were probably at Baghdad (even if Bohemond himself weren't)... is there any reference for that?