There are a lot of things that could have gone wrong here and it's hard to say exactly what happened. If I'm understanding you correctly, you're saying that your friend had lab tests done as part of a preventive visit, and was told that these were covered, but that they were not paid - is that correct?
I would recommend your friend start by looking at her plan documents to see whether or not any labs are listed as a preventive benefit. If yes, then one of two things may have happened: 1) the insurance company may have denied the labs incorrectly and may need to reprocess those claims; or 2) the doctor's office may have billed the claims incorrectly with a diagnosis that did not indicate that these were preventive, in which case they may need to correct their claim.
But if the answer is no, and there is no preventive benefit for those labs, then your friend may have been given incorrect information or may have misunderstood what the insurance company or the doctor's office was telling her when explaining the benefits. The labs might have been covered for diagnostic purposes but not for preventive reasons and perhaps this might not have been explained correctly or whoever spoke to the insurance company may not have asked the correct questions. If your friend finds that the insurance company or doctor gave her incorrect information, then it's possible they may be willing to make a correction to the claims or a reduction to the bill as a courtesy due to their error. However, since it's really up to each patient to understand what their benefits are, they aren't really under obligation to do so.
Hope this might help some.