1. Don't use SuperShuttle. They are as bad an operation as exists. They sc*ew their drivers (who are independent contractors) and that leads to a culture of hatred which manifested itself here.
2. OP should have agreed to anything and dealt with it with a SuperShuttle dispatcher on arrival at LAX.
3. Now, it's too late, but OP certainly should send an email to SuperShuttle stating the exact amounts paid.