The difference between what players think and what Peter King thinks is on about the same level of difference as how fans feel and react vs. how players do. These guys live it, we just observe from a distance. And Peter isn't even an in the trenches locker room kind of commentator.
If you listen to guys like Smerlas and DeOssie (challenging as that may sometimes be) talk about the reality of the game, they will tell you that the TJ scene is replayed dozens of times a day all across the league. Teams need to know which guys they can count on, and the same ego that got most of these guys into the NFL drives them to prove they are one of those guys. There are multiple examples last season alone of players being pushed or pushing to return well ahead of schedule to earn or retain a job or salvage a teams season. Pennington, Culpepper, Palmer, Green and even Harrison. I think Rodney and Carson are examples of players who pushed, while Green is an example of one who was reluctant to but felt pressure based not on how badly his team missed him but rather by how well they were doing in his absence. Culpepper was pushed by a team who made an ill advised committment to him. Pennington saw his contract incentivized based on playing time, and agreed to it because the alternative was losing that job. On the Colts guys found out their GM not only pushes you he takes your salary away claiming your degenerative condition is not football related and the act of driving to work is not work related. Ownership here has shown it won't take that hardline stance in most instances.
I agree that by and large guys want two things - money and opportunity to keep making it or increase their capacity to make it (here or elsewhere). Guys like Reid and Klecko can grouse about us not paying them this season, but if not for BB they'd be out of football today instead of being fitted for rings elsewhere and Deion Branch would likely be just another nice second or third had BB not matched him up with a QB like Brady. We're generally not going to be in the market for the big ticket FA because most of them are overpaid to some extent and we simply won't knowingly do that. And at the end of the day BB only really wants guys who want more than money - self motivated and preferably unselfish guys who do still crave the ring or desperately want the opportunity to prove they are more than they appear to be perhaps mired in a situation where it's hard to look good. BB and Pioli readily admit it's a small gene pool from which to select, which can be frustrating for fans and even teamates at times, but selecting outside of it is a waste of time and effort, not to mention money.