It's not the same thing, though. The other GMs aren't your employees. They're not your subordinates. They're your peers, and you depend on them. You might be working with them in the next job, because it's a tiny industry. The things that benefit them are the things that benefit you, too. It's in everyone's interest to stay cordial, at the very minimum.
Behind the scenes, everyone is just trying to keep their jobs. My hunch is that there's an unspoken agreement that you won't go out of your way to do anything to harm another GM's job security. That's IMO a big reason why offer sheets aren't done. It's doing exactly that. If you match, your cap is blown to hell and could get you fired down the line for bad cap management or simply poor team quality. If you can't or don't match, you might have just been pushed into a rebuild when you aren't ready for one. And more importantly, when ownership isn't ready for one. That's an easy way to get fired.
So this sort of thing is taken very seriously. If you do it, you broke the code and suddenly a lot of your calls may go unanswered. If other GMs won't deal with you when you need them to, you're screwed. And when the rest of the league starts offer sheeting your guys because you offer sheeted someone else's, you will likely regret you ever did.