I don't know if that's true but I don't see the relevance regardless. To me, we didn't hire Triano. We fired Watson and plugged the leak with Jay. AFAIC, if the team doesn't have to fire Triano at the end of the season, he wasn't hired as Head Coach.
That’s because all assistant coaches sign a remainder of the season contract to become the interim head coach for remainder of the season. They do this because assistant coaches generally make very little $$ so to be fair to them, they give them a new interim HC contract with increased salary due to the increased responsibility. These are typically 1 year contracts. I learned this from football intially few years ago and then someone on a different forum told me it works the same way in basketball as well.
So yes, they technically don’t have to fire the interim if they don’t want him, his contract simply expires.
But it’s similar if it was a normal headcoach who had an expiring contract as well. For example, if Celtics never re-sign Brad Stevens and his contract runs out, he won’t be technically fired just the same way you said Triano won’t be fired either if he isn’t hired as the next HC.
Think about it this way, if McDonough had went and signed Jeff Van Gundy after firing Watson, would you still not count that as a hire? I doubt you would so you can’t disqualify a hire just because it was from within the team.