Actually, a team does own a girl once she has signed an ASA roster (I would assume the same for USSSA, NSA, etc.) for that calendar year.
It has always been my strong belief that a commitment should stay a commitment from the team and from the player until tryouts begin anew in August. This is assuming the team has substantially fulfilled its promises to the player and vice versa. If a team says it will play two fall showcases and Rising Stars in January and ends up doing none of the above, then the player is ethically free to bolt. Or if the team says it will practice once a week in September through January and doesn't come close to doing so, the player is free to bolt.
But a player leaving a team simply because a better team has come along with an offer is just plain wrong, in my opinion. I would assume that player expects her team to commit to her for the year and not cut her in February if a better player comes along. If she does expect that, then she should live up to her end of the bargain as well.
The model I describe seems to be disappearing more each year. I don't know how it's going in Ohio the last couple of years, but most of the top organizations out here in the Pacific NW just recruit other teams' players all year long. I haven't recruited any girls who have jumped teams in the middle of a year, but if I am recruiting one, I will take a close look into the reasons why she jumped ship. If it is only because she could move to a better team to "better herself," I'm backing off at that point, as in my book she has just "worsened herself" when it comes to character. She might be a great player who would add wins for us, but I don't want to deal with that type of lack of character for four years.