I applaud JohnGalt for not giving in to signing a form that allowed the in-network lab to charge more than the agreed upon in-network rate. When asked to sign such a form before services are rendered, I think I would cross out the sentence agreeing to pay whatever insurance does not cover, then sign.
As for the OP, I think it is unfortunately becoming more commonplace for such pay-upfront-the-entire-bill shenanigans, then being told to bill the insurance yourself to be reimbursed. That is an out-of-network provider hassle. I fell for that last year too. And I felt cheated and deceived, but I let it go.
I think if you wanted to take action, I would make a formal complaint to the state insurance regulatory agency. I think complaints to the state medical board are only entertained for allegations of medical negligence or fraud, but I may be wrong. And I would definitely tell the PCP office that they made an improper referral to a specialist who definitely did not practice in-network billing. It makes me angry when insured patients are jerked around like this.
Now, when I make an appointment with a new doctor or laboratory, I verify with their office whether they are in-network with my insurance plan. Then I verify with my insurance what my copay is, if anything, and stick to it if the front desk employee insists I pay more. I would be prepared to call the insurance company right then and there, and have the insurance company "explain" to the provider's office manager what being in-network means.