Here is the problem with that line of thinking....there is no way for us to know.
I have been critical of Cook and some of his short comings as a player, but, I have never questioned his effort. There is no way I could know his effort. The concern about Robinson not approaching game prep as a pro was a real concern if it is still true....it may or may not be. We don't have a way of knowing.
In my opinion it is pretty unfair to assert a player isn't trying or doesn't care based on watching a few plays on a tv. A guy like Cook has some shortcomings as a player, but, he is playing against other players that are in the top portions of the top 1% of players in the sport. Any shortcomings are going to be exposed from time to time. A guy may use bad technique, may get sloppy with hand placement on a block or may lose the edge on a block for example because he is not quick or is being asked to execute something he does not excel at....it may look bad, but, it does not mean he is not trying.
Working with guys trying to improve their throwing velocity (pitchers) I have had the opportunity to see what pro guys do to work toward this end. Six to eight hours a day, five or six days a week would be the norm with the programming they were doing. That is what most people work in their day jobs of course. Nothing crazy about that. But, if you asked most people, even a lot in baseball, what do pitchers do in their offseason they would probably say, play catch and some jogging. In other words, appearances often dont mean much.
With a roster of 53 guys or whatever it is never going to be a group of 53 robots with the same work ethic, level of ability, free of personal problems, or even 53 guys that get along. It is just pretty unfair I think to single out a couple of players and basically say "this guy doesnt try"....like I said of the reporter asking about it, it is insulting really.