I'm going to play devils advocate for a moment...and probably get a lot of interesting comments. But......understand I am just looking at the facts. I made my living as a Detective for twelve years and the first thought that comes to mind is "Why is this coin being compared to the former William H. Woodin example?".
It, the Wm Woodin example, has a nice pedigree; and a note from the first noted owner saying its an authentic 1870 S. BUT it's documented pedigree only goes back to 1911. And it's documentation is not substantiated by Mint records or paperwork. Only the word of the seller of the time, regardless of any previous or subsequent positions he might have held, he was still the seller.
From just a purely unbiased view as an investigator; neither coin has any official documentation. It doesn't mean one,or the other; or both are not real. I mean we do have 1913
Liberty nickels and an 1959 Wheat Reverse Penny.
But to base your diagnostics on a coin that does not have any official documentation from the mint; and was just part of some famous collections is not absolute proof, one way or the other.
Wouldn't it be ironic if the real second example was determined to be a fake based on the diagnostics of what could have been an early 20th Century fake that somehow wound its way into the hands of a well known collector? But, surly...rich collectors never get fooled....
Just sayin.......