I doubt it, personally. If you said your biopsy came back "suspicious" or "inconclusive," I would be more likely to say that it could be something else. Saying specifically that it is Papillary Thyroid cancer means that they found cells that look that way. There are 3 (or 4, depending on who you ask) other types of thyroid cancer. Yes, you can have a false-positive, but the tests are imperfect, regardless of the result. Let's say you had another biopsy and it came back negative, you would have no way of knowing which test was right and which was wrong. The second test may just have missed the cancerous part.
Also, do you have any symptoms of TB? Have they done a TB test? Chest x-ray?
I'm guessing your doctor is recommending surgical removal of your thyroid, correct? I know it's scary, but it isn't as bad as it could be. Thyroid cancer is one of the best kinds of cancer to get. The survival rate is really really high when it is caught early and the treatment is effective and safe.
Do some research into the subject. It seriously helped me when I was in your shoes. When I was more informed on the subject, I felt like I could more fully participate in making decisions about my own care and ask questions.
What kind of doctor are you seeing? I know a lot of people recommend endocrinologists, but I think an ENT (ear, nose, and throat) doctor is just as good or better in your case. With most cases of thyroid cancer, the blood tests are normal. Since Endocrinologists aren't surgeons, you would have to see an ENT anyway.
Please feel free to post again with any new developments or if you want more information.
Good luck with everything.