The station is no longer owned by L&J Media (if you're looking at Wikipedia, it's not updated).
The FCC file for the station (and Radio-Locator) has the new owner "Local Media Boston, LLC", which appears use a national programming service called "Local Radio Networks", the current distributor of the "True Oldies Channel" and about twenty other national music formats.
I don't know whether there's a business or ownership affiliation between "Local Media Boston" and "Local Radio Networks", or what it is if so, but I would guess that the station (WMEX, "Local Media Boston") is not paying outright for the "True Oldies Channel". Maybe barter, or maybe some sort of co-ownership, local subsidiary, or franchise.
At least much of Shannon's airshifts are voicetracked. Records the announcing breaks all at once, the computer schedules them to play at the correct times, before and after the correct songs, etc... He's not doing nine hour live shifts every weekday, I heard a claim that maybe he does the morning drive portion live.
Ironic that a national company that nationally programs (their claim of) "over 1000 stations nationwide", and a local station owner that has no local airstaff on the air and airs only national programming, calls themselves "Local" anything.