Hey, I had Hurthle cells, too! Weird.
Although mine turned out to be cancer, I know what you are going through. The multiple ultrasounds, the FNAs, all that. Not fun.
Yes, it is possible to have something grow that isn't cancer. Benign tumors and nodules can grow, but not be cancerous. When my FNA results came back, they were "inconclusive" (but showed Hurthle cells) and the three ultrasounds over time showed the single nodule I had to be growing. After a year of this, my doctor advised me to have the right lobe removed (where the nodule was) and have it tested.
I asked my ENT if it is possible for a benign nodule to grow. He said yes. I asked if it is possible for a benign nodule to become cancerous. He said yes. I asked if Hurthle cells made it more likely to be cancerous. He said yes. After much research and consideration, I decided to have the surgery and the nodule turned out to be cancerous.
I think what your doctor is telling you is good advice. Your only two options are to keep testing it to make sure everything is okay or to have it surgically removed (which is probably premature in this case).
Unfortunately, you may never have a clear-cut test result that tells you it's time to have it removed. I didn't. These tests have false-positives and false-negatives. I'm glad you are doing research into the topic. That made me feel better and I felt like I could more fully participate in making decisions about my care.
The main thing to remember is that if it does end up being cancerous, the prognosis is very good. The treatment isn't nearly as bad as it is for other cancers and the tests to detect it after treatment are very effective.
I hope everything turns out well. It seems like you are receiving excellent care from experts. As long as you continue to do your follow-ups, you should be fine.