The Vikings using the franchise player tag on linebacker rather than on wide receiver Sidney Rice comes as a bit of a surprise to yours truly. I thought that, of those two players, it would potentially be harder to get Rice signed to a long-term deal, and that Greenway would be more amenable to getting something worked out without the use of the franchise tag.
However, the fact that the Vikings chose to tag Greenway rather than Rice may also be a sign of something else, and that's the Vikings' continued displeasure with the way that Sidney Rice handled his off-season hip surgery. Rather than getting the problem repaired right away and ensuring he'd be ready for the start of the 2010 regular season, Rice opted to try to let the injury heal itself without surgery, and "didn't realize" that the healing wasn't taking place until the second or third day of training camp. It was only then that Rice opted for the surgery and the eight weeks of rehabilitation that came with it.
The Rice injury was one of the bigger catalysts in the Vikings' offense being the disaster that it was in 2010, in my opinion, and opting to place Chad Greenway's contract ahead of Rice's might be a way of signaling to Rice that the Vikings weren't pleased with the way he handled things this off-season. The difference in price between the franchise tag for a linebacker and a wide receiver isn't significant, so I doubt that money was the issue when it came to this.
For the record, I never thought that it would be feasible for the Vikings to use the franchise tag on Ray Edwards. The defensive end franchise number is the highest non-quarterback figure of any position, and Edwards had a bit of an attitude already about not getting to test free agency this past season, so putting the franchise tag on him likely would have only served to exacerbate that situation.