If you’re lucky, your literature research may reveal a book published about your family done by genealogists in the past. Writing such books was popular in the nineteenth century, especially for prominent families, or descendants of early settlers of a colony, for example. Several such books exist for New Netherland settlers.
In many of these early books, chapter 1 is where the author tries to sketch the early history of the family. This is where you find claims of royal descent, of disinherited heiresses, or lost titles. Some books start with references to people living centuries earlier who shared the same last name, often in completely different places than where the earliest proven ancestor lived. Chapter 2 is where the proven line starts, sometimes with unproven claims about the link to the earlier history.
While we should verify all information we find, the chapter 1 information is especially suspicious, and usually the least documented. The grander the claims, the more suspicious we should be.
Since these early books are in the public domain, they are usually more easily accessible to current genealogists than more recent work that is up to modern standards. That has led to a proliferation of the unproven claims in online trees.