It seems odd that there is still debate as to the parentage of certain celebrities. How difficult would it be to obtain a soda can or cigarette butt used by each prince and then run a DNA test? Surely this is the next logical step for the paparazzi. And there are many questions that could be answered through this method.
Perhaps we don't see this kind of DNA snooping due to liability concerns. But is your lineage a private fact? One's purported ancestry is a matter of public record. Would a reasonable person be offended to find out that s/he had a different father? Likewise, is it any more offensive to reveal that someone's genome contains the BRCA1 mutation than it is to follow them to their mammogram or chemotherapy appointments?