All four have the potential for good story lines, but the Lions would be the least favorite for the executives making the decisions.
Giants, Raiders or Skins could all set up for great episodes. Giants would do it because they still believe they got their qb, and this show “could” help them prove it (via TV magic). And peeling back the onion on Barkley could be awesome if he agreed to it. Raiders would do it just to further build up a national viewership because their own local fans may or may not show up this year for the terrible stadium they are in. And, seeing the trio of Gruden, Mayock and Carr on the screen all trying to be the smartest guy in the room would be like watching American politics. And finally, with the NFL draft in Vegas next year the build up on Hard Knocks could be something they can’t pass up, especially after what just happened in Nashville. And the Skins, well... Snyder. Plus Guice and Haskins on the screen could be awesome for their young careers. But, would they be forced to cameo something small about the team name controversy in an episode? Some young college kids (like only 3 of them) with signs out in front of the stadium. Haha. Kidding aside, it could be a small enough reason to keep them out.
My vote is the Raiders.