The key is who wants to make the change and how much they are wanted at another club. Yes it's true that the club with the current contract has to make sure the player is paid the full value, which is why when you see a club offloading a player, they pick up part of the salary.
As a matter of the NRL rules, this doesn't change just because it's the player asking, but as a matter of actual reality, it does make a difference.
By way of example, if Bird wants to back out but Brisbane don't really want him to, they simply say "sure you can go, but we are not paying any of your wage" which means Bird can only go if he finds a club willing to pay his full salary.
Side note: I think the rule needs looking at as it could actually disadvantage a player. If Bird wanted out (just an example) and Brisbane were willing to let him go as long as they were not having to carry part of his wage, and Bird gets an offer from a club that is 150k short of his Brisbane contract, if Brisbane won't pay the 150 Bird is stuck where he is. Even if Bird would be happier to go to the new club and accept less money, the rules don't allow it, and take away his choice
I don't think that's OK