The MBTA does fall under the executive/governor as it is under the MassDOT umbrella, and the governor selects the MBTA's manager, and, at least under Baker directly appoints the members of the board of directors who have direct oversight. The legislature controls funding/purse. It very much is on both parties. That said, Healey has been governor for like 2 weeks and immediately launched a search for a new GM. Nothing she can really do at this point and trying to put the current MBTA's problems on her is laughably stupid.