Sorry to hear of your issues. I had the CCT fail on my '12 at 89k. It took 4 months to get it fixed under warranty. (pistons, valves, lotsNo "wear" is covered under warranty. There are no specs for the cam chain in the factory service manual, so that's BS on your dealer's part. If it's "damaged", that's a different story, but they will need to send the part to Yamaha most likely unless there is a regional rep close by to come look at it in the shop.
If they didn't take the valve cover off and tried to just swap the CCT, it is possible for the chain to slip. There are some good posts on the forum about how to do it so you minimize that risk. There is some debate over what the manual says in terms of required steps. If the chain slips, it pretty much requires the removal of the valve cover to see the timing marks and re-align everything, which means they will need to order a gasket or two.
I have the '14 CCT in my '12 now and while my bike rattled on start up from day one, the motor is much quieter now after the repair and with the new style CCT. I have no reason to consider a manual CCT. Nor any desire to adjust it as often as I probably should if I had one.
Good luck and I hope you are riding soon.