We could suspect this since LOC... it was always pretty obvious to me LTT couldn't have been as white as snow when it came to the betrayal of his lieutenants (or in how he dumped Mierin, for that matter), and watching him with Taim and others (that's when LTT's personality started to come out), it was easy to see he was full of himself and could be very arrogant (and Moghedien implied he was also the self-righteous type too). It's said he showered Bel Medar and the rest with honors, but clearly like Rand began circa LOC, LTT always made sure it was clear where the honors came from and that himself was above them all... the same attitude he had with those pins... he didn't wear them himself, and one of those pins was his own sigil as dragon. He made wearing his sigil the greatest honor at the BT...

It doesn't make Barid Bel Medar much greyer, though. The guy is still the same: Demandred chose the Shadow over being second for the Light. That he felt a slight from LTT or not, that's no excuse to betray the whole Light for it. LTT might have been able to avoid that and keep Bel Medar loyal, but in the end Bel Medar made the decision he made and traded the lesser glory on the Light's side by entering the race for who would be the most infamous on the Shadow's side, and he climbed the ranks really fast it appears.

And let's not forget: Rand is into a self-blaming mood lately, but one of the Chosen once implied Demandred doesn't have that much cause to hate LTT so viscerally.