I installed a Hitch Doc on my 2011 XC, easy enough. Only problem I found a few of the supplied bolts were short, called them and they offered to send replacements, I had already bought some new ones. They stated the proper ones would be sent with future hitch packages.
Did not have to remove the tire, just the bags and the seat.
You would have to do some checking, I doubt that there is any difference between a 2011 XC and a 2012 XCT as far as mounting a hitch. This is my third Hitch Doc, never a problem with the hitch.
2008 Vision Black gone 2005 TC- Sold
1963 Triumph Bonneville,not sure on color-be awhile
1983 XS 650 Custom Midnight Gold
2007 Ural Patrol Black-Sold
2011 Cross Country White and Silver
2012 Cross Country Red and Silver--Hers
A bunch of other bikes over the years, mostly all good
Life is short, eat dessert first, simple enough.
N/E Georgia and my garage