Andy, you are right in that is what the maintenance manual says, even the parts catalog says the same thing. The thing to remember is the MM and PC for the CTLS was largely copied from the CTSW, instead of a complete rewrite. There are quite a number of inaccuracies. Having changed nose tires on both the CTSW and CTLS I can assure you that the CTLS uses a 6" wheel with a 6.00x4 tire. Here is a good article explaining the changes between the CTSW and CTLS.
https://flightdesign.com/files/Ed%20Dow ... S-0508.pdf
The information in that article is a bit suspect. It's an article in EAA Sport Pilot, and is not an official FD document. I think the line you are referring to is: "The nose wheel is now the same size as the 6.00-4 main gear". Except the mains on the CT have *never* been 6.00-4. They have been 4.00-6 for standard gear and 6.00-6 for Tundra gear. So far I have not found any reliable, official source that states that the CTLS standard nose wheel is larger than than that on the CTSW.
Maybe somebody with a non-tundra gear CTLS could chime in with their nose wheel tire size? It might be hard to find one since most CTLS (and CTSW for that matter) came with tundra gear.