I agree. Jason LaCanfora is probably on the cheese factory payroll as well. Teams gather information on other teams and a source of the information are the reporters. It isn't such a big step to think that known devious operators like Kraft and Belichick have just extended their scope via twitter.
I'm suddenly reminded of a scene in The Godfather after Sallazzo and the Police Chief were murdered, when Michael Corleone asked Tom Hayden if the media would be interested in a story about a bad cop who got corrupted, Tom admitted yes, we have reporters on the payroll.
Despite his image of kindness, decency and propriety, Bob Kraft operates like the Godfather of the NFL. Miami Dolphins are pretty low on his radar but maintaining dominance in the AFC East has been the cornerstone of their long success. Getting his mignons to throw the reporters some bucks for information and disinformation sounds possible/likely.