Is the players.txt meant to be a a list of current players connected to your server? Most of the time there are player names in this file that are not on the server.
It does indeed show the players in the server. Because of a bit of lag you might also see players that aren't in the server at that moment. When you have it open and a player leaves he will also still be on the list, until you close the list and open it again.
players.txt what is it?