This seems reasonable. And the tweet may not capture the whole rehab arrangement.
As far as having access to the facilities, it could simply be a standard protocol given the lengths of the rehab and the contract not lining up. In addition to that, there are the protocols of COVID (which, OK, Texas and all, but maybe MLB's protocols).
And given Verlander's status, the Astros may have decided to keep their resource intact for their season and allowed Verlander to seek a rehab team that he was comfortable working with. The rehab folks can work back and forth with the Astros on different rehab programs & guidelines for pitchers while the rehab team does the day-to-day rehab work.
Or maybe the Astros did kind of pull the rug on Verlander, but he's cool enough to realize that he's an older free agent coming off of TJ and getting into a public word battle doesn't make a whole lot of sense for him. Remember, he's preached from the pulpit before on domestic violence and cheating in baseball, but when those questions got turned around on him in regards to the Astros trading for Roberto Osuna and the whole sign stealing deal, he kind of turtled up a bit.