I think all this speculation on what his relationship with the AD was and how all that played out is really moot. We really don't know what happened, and everything we hear will either be 1) hearsay or 2) biased - likely both.
here's what we do know - the lowest guaranteed coach salary in the big 12 in 2015 (for schools for which we have data) was Tubby Smith @ $1.7M. Granted I only saw data for 8 schools, but i'm guessing the last two aren't significantly lower.
I think it's reasonable to assume salaries haven't gone down in the last couple of years. The would make BU - by far - the lowest paid coach in the big 12. That for a coach that was one of the seven school in the conference that secured a tourney berth in his first season there. If you're the AD for OSU, you should fully expect the coach to expect a renegotiation of the contract, regardless of what the contract terms were. It's like saying Greg Gard wouldn't be justified in expecting a renegotiation even though he took UW to two straight S16's and is supposedly being paid <$2m/yr (unless it's already happened). Alvarez would be delusional to not expect that.
So with that laid out, regardless of what the relationship between BU and the OSU AD is, it is fully reasonable for him to test the market and see what he's worth. If the relationship was strained, that doesn't help things.
I obviously don't know BU in person. What I do know is that his mentors (Huggins, Martin), are not exactly the most outwardly friendly people in the world. He does give off a similar vibe, so we'll see how that plays out. But that doesn't change the facts of how this hiring played out. And OSU can't be mad about that just looking at the facts. The OSU AD shouldn't have given him the opportunity to test the market if he really wanted him to stay. But that is exactly what happened. Even if BU is the nicest guy in the world, i would still expect him to do the exact same thing, because it's the smart thing to do given the circumstances.