Mike: As a general rule, the airport "sponsor" / local government has authority over surface issues, principally including noise, environmental, and security, while the FAA is responsible for what is in the air. Security responsibilities for physical assets (planes, buildings, parking lots) at airline-served/Part 139 airport are the sponsor's responsibility. Passenger screening, on the other hand, is principally a federal responsibility.
TSA (different folks that those that handle passenger screening) and FAA both have security manual/procedure requirements, as well as emergency plans dealing with a range of security and non-security items. The sponsor writes them (or hires it to be written)

and tailors them to meet the available resources, needs and wishes of local management. These manuals are then subject to page by page review and approval by the feds. (Literally, every page is stamped, signed, and dated.)
The methods chosen for the security package involve many things:
- badging requirements (photo only, digital, etc)
- gate security (human monitors, electric gates, manual locks, cameras)
- aircraft security (prop locks, cameras, roving patrols)
- responsibilities of local police vs airport police
- and lots more.
Each airport has different programs for its needs and, once approved by the TSA, become binding on the airport.
MASSPORT has been tangling with prop-lock requirements for a long time, but I don't know the current requirements their various airports. (For many years prior to 9/11/2001, MASSPORT had a reputation of being expensive and non-accommodating to general aviation aircraft. I suspect that it has gotten worse up there for the small GA operator since the creation of TSA.) In any event, the prop lock requirement is a local one to MASSPORT -- one that they have authority to do, and might now be required to impose if they have made it part of the security plan at that airport.