There are so many reasons you say this. (Notice I didn't say do it).
If you have a top 5 pick, you need to show as much interest as possible in every projected top 10 pick. You want any team below you itching to get that one guy, to trade up with you or even above you to get that guy. You make teams that want someone to pay for them. The interest you show should be equal. You don't want to fawn over that one guy and cause someone to jump ahead of you and take him. You also don't want to fake so much interest that everyone knows you are bluffing.
Another reason you do this if the Redskins see only 3 non QBs they like with their pick at 5, then the best way to guarantee they get one of those guys is to get a QB to go ahead of them. Or maybe they really like one guy, but he will go ahead of their slot. Saying they want Mariota will cause a team below them that really wants him, to jump up above them. That moves one of those guys down to the Redskins slot.
If the Redskins say they have no interest in Mariota, then that is one more spot off the board where you know he won't go. That makes the cost it takes to get him go down. Because the further down the draft board a guy falls, the less it takes to move up from say pick 20. It may be too much for the Eagles to go from 20 to the top 5. But maybe not too much to go from 20 to 6, or 20 to 10, or 20 to 15. By signaling interest in Mariota, the Redskins increase his demand and cause teams to take action.
Now, the Eagles or any other team can call the Redskins bluff and see what happens. I would not want the Redskins to take him to just to keep up that bluff. If the Redskins really like him, they should take him because he is the guy. I think the worst case scenario for the Redskins, is no one take Mariota, and he falls to the Eagles at 20. If at all possible, teams need to make the Eagles pay to get him. But don’t take him because you are bluffing the Eagles and want to keep him away from them.
The bottom line is, you need to show you have as many options as possible.