Under this scenario you're NOT paying $100 to that other credit card, (Navy Federal is).
Think of the childhood game of Musical Chairs. Every time the music stops someone doesn't get a chair.
Play this game with CC issuers long enough and eventually you won't get a chair.
Balance transfers can help you save money under limited circumstances, but unless you have a reasonable plan whereby you can eventually pay back ALL the money you've borrowed on a revolving basis, the BT game isn't a whole lot different than "re-arranging the deck chairs on the Titanic"
+1