The best case they had was a post Peter made on Bitcoin Talk where it appeared that he was posting a follow-up thought to something Satoshi wrote about transaction fees, suggesting he was logged into the wrong account, and then he stopped posting around the same time as Satoshi and didn’t return for several years. 

 I can see him being part of the group that made up SN and had write access to that account but Peter isn’t the kind of guy to head up something like bitcoin. Not because he’s not smart enough but because his heart wasn’t (and still isn’t) hard enough to light that candle.