Breakdown

'No, he can't be Tyr,' Haylee still refused to believe Kyran's claim. If she did, she had to admit that she had been deceived- not only by him but by the Conclave.

Correct. The Conclave was involved because right from the start they had been proactively protecting 'Disciple Tyr.' Not to mention, when Gael sent an anonymous request to hunt down Kyran, 'Tyr' was the first one to submit a report on the latter's possible location. If they were the same person, then it meant they got played by the Conclave and Kyran— or could it be that the Regis Clan knew this would happen right from the start and had conspired with the Conclave?

Haylee also had to accept that apart from them, the Templar Code already got the Regis Clan on their side— or, was it the other way around? Could it be the Regis Clan won over the Templar Code and had Tritus swear allegiance— probably through something similar to a Soul-binding, which was why she could not see through him?