The statistical metro is probably the closer match to the Boston that controls the state than the proper city.

That's true but the parent was asking how many people don't live in Boston but are effectively controlled by the politics there anyway. And the statistical metro is in some sense a measure of the area/population that can be thought of as associated with Boston. (i.e. more or less by definition, the people whose politics/economics are influenced by it)

But that's kind of the rub -- people in Hingham might carp that they don't want to pay for the T in Boston, and yet their own prosperity comes, in part, from having a nearby city with well-funded public services