The key is in understanding Tom as master. Tom is master of himself, not of Middle Earth. That's why the ring has no impact on him. The ring can't master him because Tom is master.
Tom is a person who is totally at home with who he is and his place in the world. He does not desire adventure for its own sake, nor fame, nor glory, nor wealth. All he desires is to love his lady and be loved by her. He has his part and doesn't try to go playing someone else's. In Christian terms, he doesn't see every opportunity as a calling, but waits patiently until he is called. Because he so thoroughly trusts in G-d for who he is, he can resist the opportunity to try to step outside of his calling.
Shalom.