The difficulty with relating Ms Crawford to Charlemagne is that in those programs there often are loopholes with little written documentation and a lot of, what the Germans say,
hineininterpretieren (interpret these holes so that you get the desired outcome).
In comparison royal genealogies are extremely well documented. All current royal families, name them Monaco, Sweden, the UK or whatever have excellent archives and can, step by step, with requested documents and evidence, work towards Johan Willem Friso of Nassau, Prince of Orange. All based on actual facts, original registries and without
hineininterpretieren.