Do Law Offices affect ties you're not part of?
The rules seem pretty clear about this:


  In addition, at the end of the game when goals are being scored, the player with a Law Office scores points if he is tied with another player for achieving one goal (public or his own private goal, which he picks from any of his tied goals) as if he had won it. If two players have the Law Office, they may each score the same tied goal.


(emphasis mine)

So no, it does not let you win a tie that you're not part of. (It doesn't work the same as your example from another game.)