Carrying locally produced (read: hire CBS Sports to do the game, but brand it as "Titans Football" instead) games has nothing to do with carrying the NFL Network feed of a game over your local airwaves.
That's a separate contract, bid on separately from the contracts for producing and carrying preseason games.
For instance, there are markets where one channel has the deal to re-broadcast ESPN Sunday Night Football when their home market team is on, but one of their competitors has the deal to carry NFL Network games featuring that same team.
Trust me...I'm a doctor (er, professional TV guy.)
Since I can't bump the last thread on the subject, TMQ's back on NFL.com (NFL.com). (For some reason, clicking on the link on the site's front page in Mozilla won't work, but everything else does... mayhaps it's the ad-blocking?)