In a comment below, Jim Conway offers some data from the Commonwealth Fund that sheds light on the question posed. I have copied the summary above.
Recall that the proposition was: "There is lots of evidence that Massachusetts health care is the best in the country." We get excellent grades for access and equity. This is not surprising given the state's universal insurance coverage law.
We do well on "healthy lives," too, but I do not know how much of that derives from the health care system as opposed to relative lifestyle (smoking, obesity, and the like) in the Bay State.
But we clearly have a problem when it comes to overuse of the hospital system. Also, the performance with regard to standard indicators of care is not exemplary.