I believe that despite the claims of many early American families to royal ancestry, the vast majority of trees with those entries contain unsubstantiated matches. I can usually determine that easily be looking at a couple of early entries and seeing that they contain no original sources.
There is a line in my wife's family that traces to the Plantagenets, however when I tell people this I always say that at some point research merges with myth, so anything that far back is highly speculative.
I do acknowledge that there are exceptions to this, but they are unlikely to be related to my Irish immigrant family!
Jim