I had a screw in one of my RFT's 4 months ago. I called my dealer and got a similar response. So I dug into it. Here's what I learned.

It's OK to repair a RFT if the nail/screw isn't near the edge AND the tire hasn't been driven with little or no pressure. The problem is that a repair shop can't tell if you've driven with little or no pressure in a RFT like they can with an ordinary tire. So the safest thing for them to do is refuse to fix them. Some independent shops will fix them. In my case, the TPMS warned me about the low tire but the pressure never dropped below 28 psi. I fixed the RFT and it's been fine for 4 months.