That is correct with the THSBA, you may fish with the closest school that has a team, if allowed by the school. Some unfortunately do not allow other school members to participate in their schools teams. But also, you can create your own team without the school as long as you verify the passing grades.
I cannot speak for FAN or THSBA, but I know SETX will allow a kid to fish with the closest member school to that kid "IF" that school will allow someone in from outside their district.
My suggestion, start your own club or organization "East Elm County Jr Anglers" for example. I believe I do speak for FAN and THSBA in saying that you do not have to be in a HS CLUB, just a club in general.
Bottom line, like Ken said above, we just want to put kids on the water the best way we can.