That's so true, there was a move by teams a few years ago to give the players more time before the reporters came in after the games, but the NFL nixed the idea when the media complained about their deadlines. The league sided with the media by saying *they* are here to help sell the product to the fans.
In a lot of ways I think the owners are with the players on this issue, but the league sets the policy. Most of the time the players don't mind the local tv and newspaper folks who they deal with all the time, it's the "special" ones like Sainz et al who cause the problems.