Bright Watson - Conflicting fathers

Hello, all,

This profile for Bright Watson is showing two different fathers:

1. Rev Anderson Walsh Watson
2. Nathaniel Watson

In reading the notes on trees from other sites, it looks like Anderson is the more common choice, but that a number of researchers are adamant that Bright wasn't a son of his because Bright doesn't appear in family records. Other researchers have said there's no evidence for either, or for Sarah P Watson being Bright's mother.

I am unable to find any primary or solid secondary sources stating which one is correct, if either. Do any of you have sources for or against either candidate? Let's see if we can sort this out together.