“Genealogy without sources is mythology” is one of those cliched phrases that reminds us of the importance of having (and citing) sources in genealogical research. Like most quick, off-the-cuff remarks, the reality is slightly more nuanced.
Just because you don’t have a source for a statement does not mean that the statement is untrue. To be certain, your case without a source is non-existent and if there’s no source it makes it significantly more likely that someone could easily prove you wrong. Having a source for a statement makes it less likely that the statement is incorrect.
But…and it’s a big “but.”
Just because you have a source does not mean that the statement is correct. Sources can contain errors. The genealogist needs to determine the perceived reliability of statements made in sources by determining (if possible) the informant for the specific information and how likely it was they had first hand knowledge of the information contained in the statement they made and that by the time their statement was being recorded their memory had not faded or they had a potential reason for providing incorrect information.
Genealogy research is not always cut and dried. A researcher needs sources, but just because you have a source for a statement does not mean that the statement is correct.
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