Yes they absolutely did or why would you even have to worry about what you're paying them?
The cap can be manipulated to fit what you want into it. That doesn't mean you don't have to work with it. It does exist.
Let's take the Cooper contract as an example. The Cowboys could have restructured to move $15 million, just like the Browns did, and kept him. By moving the money, you increase the eventual dead cap hit. You can absorb that hit by more restructuring, just like we did with Lawrence's contract, especially since he wasn't living up to it, to make room for Gregory, but that creates more dead cap hit that you'll have to absorb with other restructures. The fact that you can do that allows teams to manipulate the cap for years, making strategic moves to absorb those dead cap hits. However, when a player isn't worth his market value, there's no reason to keep pushing those dead cap hits forward because it isn't worth it.
The idea that you can easily manipulate the cap to do what you want doesn't mean it is practical or wise to not worry about what you are paying. But how much you pay is more about what you believe the player's value is than how much salary cap space Over the Cap says that you have. Every team can make more cap room at a moment's notice.
