Jake Peavy may block a trade to the Braves, because the trade weakens Atlanta!

"Escobar's a pretty good player," Axelrod said. "To be honest, Jake and I have said, 'If that kind of trade gets made, who plays short for them?'"

...

"One of the things we will want to look at some point is, 'Who are you giving up? How much are you weakening your team to make this deal?'" Axelrod said. "If Team X trades three starting pitchers and a starting shortstop to get Jake Peavy, that lessens their chance of being a successful team."

I don't remember a player using his no-trade in this way. Sure, they may prevent a deal to a non-competitive team, but I don't remember one judging the competitiveness of the team based on who the acquiring team traded away.