Another one chiming in. I used to work in a garage and personally did a lot of tire repairs, but never on a RFT. I am not living in the same city now, and so don't have access to that shop. I had a flat on the Z4 with a RFT. I went to a local tire store certified to fix that brand of RFT (I think it was Bridgestone). They showed me the factory instructions for different brands of RFT, and all are different. Your BMW dealer is not a tire store, and will follow BMW instructions. Nothing wrong with that, but you may object to buying a new tire at parts department prices.

It is not about how much tread is left. As other poster said, it is about where the puncture is (not near the sidewall); if it is a puncture or a cut; which brand of tire it is, as some can't be repaired; and most importantly, how long you drove on it flat, potentially damaging the integrity of the tire from overheating. It is because of the last point that many shops won't repair them, they simply can't be sure in many cases that you didn't drive on it and trash it, and it is potentially their liability if it blows on you. If the tire looks damaged they can refuse to repair it, but if the tire doesn't appear damaged there is still some risk to them, as the damage may just not be visible. My tire store asked me how long it was flat, how fast I was going, and my answers gave them sufficient confidence to do the repair and warrant it.

If it is fixed, make sure they don't use a standard plug (from the outside). The approved repair for many RFT models is a special plug that looks like a mushroom, is applied like an inside patch, and which is drawn through from the inside to the outside.

I paid $42 CDN for the repair, including balancing.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue