I had a similar experience at NTB with my 2004 coupe. Took it in for 14,000 mile rotation, saw a nail head in a tire and asked them to check it. Turned out nail wasn't all the way through tire but they took tire off to check it. Took him FOREVER, especially attempting remounting. Then they called me - inside tire sidewall was split wide open. They blamed it on dry rot but I blame it on inexperience. Since there is no spare cost me $150 for cheapest tire they had and I got out fast, never to return! Highly recommend professionals.