When I enquired about having CC2 fitted my dealer spent ages hunting around for stock, there was none in the UK. They suggested various others and were open to any I requested but I went with ATS in the end.
I'm not 100% sure every dealer fits tyres themselves or simply farms it out. Either way, in my mind, the dealer takes full responsibility for the work, so even if they don't fit themselves in their own workshop, any issues would be resolved through them. My dealer also price matched, this was a couple of years back ...