Points and Score are not the same.
Points are a value you award to players during the tournament. They can be awarded by setting values on the Game tab, such as "Points for buy-in", "Points for rebuy", and "Points for hit". You can also set the "Points for Playing" formula to award points using a formula.
Because you award points during the tournament, you can have different methods for awarding points for each tournament. For example, in your first tournament you may only set the "Points for hit" to 1, and thus players will get 1 point for each player they bust out of the tournament. In your second tournament, you may set your "Points for Playing" formula to "n-r+1", which gives points based on your final rank in the tournament.
When you run Stats, you can use the Tournament Score formula in exactly the same way as Points for Playing. The major difference is that there is only one Tournament Score formula, so it will be the same for each tournament (versus the Points for Playing formula which can be unique to each tournament).
The Overall Score formula provides a way for you to combine the Tournament Score values to arrive at a final "score" for each player.
So, the "Points" column you see on the Stats tab is the sum of the points for each tournament the player participated in. It technically doesn't have anything to do with Overall Score. Is this where you are seeing "0" points?