> I would never have left my prior engagement if my would-be boss had not okayed it (we had a very long conversation at the time).

Once you broached the subject, did he really have any choice? At that point, he has to question whether your heart would be in it if you came to work for him, and whether you might bring down the rest of the team. At this point, you are likely getting the OK regardless of whether it is just a minor inconvenience to him or a major blow.