HBO believes that Peter Todd is Satoshi Nakamoto for several reasons: misusing his account to reply to Satoshi Nakamoto's posts, etc
According to @tier10k's summary, the HBO documentary on Bitcoin attempts to show that Peter Todd is Satoshi Nakamoto, the founder of Bitcoin (which Peter Todd himself denies). Some reasons include:
In 2010, Todd (using a new account) replied to a post by Satoshi Nakamoto on the Bitcointalk forum.
HBO claims he misused his account to complete Satoshi's post;
Both accounts ceased to be active after a few days.
Todd later implemented the "Replacement at Cost" (RBF) concept discussed in that post.
Separately, one document provider claimed that Todd used the pseudonym "John Dillon" to promote RBF. Both used British/Canadian spelling. Moreover, Satoshi's posting schedule coincided with what the document provider claimed was a student's schedule, with more posts on weekends. Todd has discussed "sacrificing" bitcoins; this may refer to the destruction of Satoshi's bitcoins.