As a matter of fact, I have seldom seen a claim to royal ancestry that was adequately sourced or had any sources at all. This lack of sources is much more common in countries such as the United States, where royal descent is viewed differently than it is in a country with a reigning monarch. I am reminded of the series of blog posts that I see from time to time asking if you are related to some famous movie star or political figure or another. There is an underlying, incorrect by the way, assumption in all of these claims, that the pedigree showing the relationship is accurate and correct. You might be impressed to be related to someone important, but how reliable is your own pedigree? How carefully has the connection been established?
OK, to start out, kings and queens had children just like the rest of the population. So, it stands to reason that their descendants can trace their ancestry back to some king or queen. What is not usually carefully researched by the claimants is each step in the relationship, even when the supposed relationship comes from an "accepted resource." It is also apparent that most of the discussion on this topic is by people who know little or nothing about doing research in the claimed royal lines. It is far different for a careful researcher in England to claim royal ancestry than it is for someone from the United States, who sees an online family tree showing royal ancestry and copies it.
Another crucial point here is the time period of the claimed connection. Many of the connections I have seen to royalty, make the connection back in the 1600s or even the 1500s when the research is much more difficult and errors are more common. There are absolute limits to the accuracy of any genealogical claim that goes far into the past. A recent book is cited by Nathan W. Murphy of the Family History Library in Salt Lake City, Utah in his post "I Have My Family Tree Back to Adam and Eve" Part 2: (I suggest reading Part 1 also).
Family Trees: A History of Genealogy in America. By François Weil. Published by Harvard University Press, Online bookstore; 2013. ISBN 9780674045835. 320 pp.
In that book, the author, François Weil, Chancellor of the Universities of Paris, as quoted by Nathan Murphy, states:
Genealogy was originally the prerogative of kings and princes. The oldest surviving royal genealogies in Europe go back to the sixth century A.D. for Gothic sovereigns, to the seventh century for their Irish, Lombardic, Visigothic, and Frankish counterparts, and to the eighth and ninth centuries for Anglo-Saxon and Carolingian kings. (pp. 10-11)In doing any research in this area it is important to rely on the most recent and reliable sources. Any pedigree dating back to the 1800s or 1700s is suspect merely because more current research may have corrected earlier errors. Copying an undocumented pedigree from an online family tree is misleading and a total waste of time. Bad genealogical practices are bad whether or not they produce a connection to a bank robber or a king.