Broadsword:
100% accurate.
Read the wiki, nowhere does it say you need a CAT 2 cable for 1080p, why? because its not true.
If you want 2160p, then granted a CAT 2 cable is needed, but only up to lengths of 7.5m, you won't find a CAT 2 cable over 7.5m.
Also, theres no such thing as a CAT 1.3 cable, that's referring to the HDMI port nothing to do with the actual cable.
I've done a bit more research and looks like you're right.

Even the HDMI website says that most (probably all) cables will work at 1080p if the length is less than 5 metres.
Not sure what the CAT 1.3 part is about. Can't see that in the OP at all... It says "HDMI v1.3b Cat 2". It's probably more suited to a 30" PC monitor.