Please speak with Tricare before believing the hospital.
Sometimes a hospital's billing and the insurance payment cross in the mail, so it could be that they have not yet received full payment, or they may not have submitted all the charges yet (even if the customer service rep thinks they did). Hospitals bill according to their billing cycle and sometimes late charges are posted after the initial billing, because they are discovered 'late', after the initial billing.

Another option, to make sure you are getting the correct information and that you understand the reasons, etc. is to contact the patient accounts supervisor for a full explanation.

Another option is to copy the bill you received and send it to Tricare with a note about your phone call, the date you called, who you spoke to, and what they told you. Ask Tricare to follow up on it.

A last option, and it works well, is to file a complaint with your state's insurance comissioner. Those complaints affect the insurance company's rating, must be handled quickly, and must the resolution must be approved by the insurance comissioner. Keep a copy of this complaint for yourself.

I hope this helps.