It doesn't make any sense that Barry would have told anyone he was at any kind of firefighter training when he knew full well, numerous people knew exactly where he was, because he made dang sure, numerous people were going to know where he was.
From the desk clerk at the hotel, to CC, MG, JP and whoever else sub-contracted that Broomfield job to him. I do suspect that the entire Broomfield job that weekend, and everyone connected to it, was his pre-planned alibi.
I suspect, TN (or another family member) did not know for sure where he was, and he might have been the first person to say he was out of town on business, and that quickly morphed into FF business.
jmo