I am assuming they threatened to sue of the papers published stories of infidelity. So they haven't. Which also suggests their sources are not iron clad.
The more I think about it, the more I think his affair is unlikely. There is something else going on, but not that William is shagging rose. Could be genuinely bad or could just be usual issues between people blown out of proportion because of who they are. Hell, if me and/or The woman from the school playground with whom I had a large public fall out were famous, who knows what would have hit the press.... (and, interestingly, while there was no issue about our respective husbands, it would have taken very little creativity to make it seem like it was...)