If you do some study on Brouthers and his life, its hard to imagine anyone would have
a. Known where he was in the 1910's to ask for his autograph
b. Cared about his autograph (people were not really collecting sports autographs in 1919, let alone those of former players)
c. Has the foresight to get his signature on a ball
etc. etc.
You basically just have to assume that every single signed ball from before about 1925 is fake until proven otherwise. People just were not getting autographs on baseballs like that back in the day unless it was a "Trophy Ball" such as the last out or whatever and they almost all come from the family. Even team signed balls back then were basically trophies and that is why so few of them exist. There are exceptions to every rule, but not many.
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