>Trademark registration for Clark Stanley's Snake Oil brand Liniment, June 12 1900. Library of Congress. Public Domain

I don't read the trademark registration as "snake oil" brand, it looks more like "Clark Stanley's" brand. The word brand should follow the trademarked name, and while this application does not contain the term brand, up at the top it says "Trademark. Clark Stanley. Linament."

the article starts out "over the 19th Century", and this trademark is from 1900, so a latecomer to the snake oil market, unlikely to be able to trademark the term "snake oil".