"Channels" is a bit like "The smile that says..." in that there isn't actually any connection, but the reporter/editor desperately wants there to be one.
Princess Diana was one of the most photographed people on the planet. The chances are that whatever Princess Margery or whatever her name is wearing, Di wore something similar at some point and the photo's on file somewhere. Dresses, jeans, swimwear, assless chaps, you name it.
Of course, the Diana connection will help raise interest and shift copy. It also feeds into the tabloid narrative that Kate is somehow Di reborn, and who will lead the monarchy into a new and wonderful future. While, er, shagging her own son. Erm. Of course, there's also the Cinderella myth as well. In which an attractive woman from the right social set can catch the eye of a scion of a very media-savvy royal house.
This is from the same media that laid into Hilary Mantel for describing Kate as being not much more than a clothes horse, baby machine and projection screen for our fantasies.