Pretty sure that would be a hard case to make when it concerns a player with a NTC.
If he thinks Houston sucks, he's really gonna be miserable playing for Belichick. I think a lot of players have seen Brady leave NE and be much happier and still win. They know how, despite winning a lot with Brady there, the Patriot Way is miserable. Why go there when you can win and not be miserable in plenty of places. I mean, if it was the only place left that would trade for him, he'd go there, but there will be lots of teams offering their first born child to trade for him.
The Pats probably won't pursue him more than just kicking the tires. And even if they did, they won't be anywhere close to the best offer. The Texans have no motivation to take anything other than the best offer unless it's from another team in their division. There are many teams that can and will offer more. What motivation would Caserio have to take a worse offer to help another team in the AFC?