Birth Control Bar? I always thought bars CAUSED many pregnancies! Who knew?

You should contact a TRI-CARE patient services rep and ask them. Insurance policies and what they cover are often complicated.
It may be that the bill is covered, but all providers bill the patient first unless you are seeing an in-network provider. It may be up to you to file a claim for payment.
Have the rep explain why you are not covered if that's their position. Ask for specific sources in your policy and any coverage limitations they are citing. Keep the names and phone numbers of everyone you talk to, in case it turns into a run around.
Insurance providers always put the phrase "any other insurance you have must pay first." If they all do that, of course it becomes a catch 22 unless you have only one insurer.
Even if the insurer agrees to pay, you may still have co-pay and deductibles to consider. For instance, if you have an annual deductible of $500 or more, and this was your only claim in 2016, you have to pay regardless.
As Q stated, YOU are ultimately responsible for the bill getting paid. Either do the work to get the insurer to make payment, or just pay it and move on.