I don't think it's an issue with windows 10. I have windows 10 64bit enterprise on my main PC, 10 profressional 64bit on my parallels bootcamp installation, 10 on my dad's PC, 10 on my Surface, and have no issues with any of them. My daughter's windows 7 machine had the same problem you are referring too and it was because her OpenDNS was blocking the teamviewer from seeing the internet specifically. Her computer could get to some internet sites, just highly restricted - TV being one of the restrictions. I added teamviewer.com to the never block category - problem solved.
So it sounds like to me that maybe there's a host file that needs tweaking or maybe some kind of internet filter that's blocking traffic for the TV checkin process (to see if you have internet or not). Sorry this doesn't directly solve the problem, but at least you can rest more assured that windows 10 shouldn't be the problem.