There are “genealogists” who can show any paying client to be descended from whomever they want. If I wanted to be a descendant of Mary Queen of Scots, voila, *some* genealogist would draw that line. This particular genealogist’s bona fides bear a look.
My father paid several Scottish (and state approved) genealogists in the 70’s to do family research from the original records.
After the internet (and the LDS church) put copies of the original documents on-line you can see a lot of “wishful thinking” in the reports he received.
An interesting thing about almost all of the Puritan era genealogies (1620-1670 or thereabouts) is that they are only 4-5 generations away from the Plantagenet royal lines.
The Plantagenet dynasty, of course, fought the bloody War of the Roses over which branch would rule England only to yield to the equally dysfunctional and much shorter lived Tudor dynasty, when Henry VII was victorious at Bosworth Field.
The Plantagenet's had dropped scores of illegitimate children (along with a lesser number of the legitimate variety) into the bloodlines of British Isles, many of whom can trace their lineage back to the most reprehensible English monarchs like John I or Edward I, who were famed for spreading their seed about.
One of the few positive contributions of the Tudor line was to make appointments based on merit rather than lineage as the rival Plantagenet's greatly outnumbered the Tudors and generally did not get installed into positions of trust until after the reign of Elizabeth I, the last Tudor monarch.
While some of the Plantagenet line displayed loyalty to the House of Stuart, especially James I, who wanted to pacify and unify the country, a great many more rebelled against the excesses of Charles I and Archbishop Ladd, the first great wave emigrating to the new world as persecuted puritans in the 1620's and 1630's and the second after the restoration of the House of Stuart in the late 1650's thru 1670's, when the House of Stuart was finally booted out for good and the American colonies became as much a dumping ground for undesirables expelled from the old country as a destination for religious refugees.