The person Poirot accused isn't really the killer.This is a professionally published WMG by French writer Pierre Bayard. He proposes that while Dr. Sheppard really was Mrs. Ferrars' blackmailer, he wasn't the killer. The killer, he says, is Caroline Sheppard. Having found out that her brother was the blackmailer (remember, she was the town gossip) and that Ackroyd was about to find that out through the letter, she sneaked onto the estate after the doctor left, then killed Ackroyd to protect her brother. Dr. Sheppard, realizing that Poirot thought he was the killer, and facing prison time for blackmail either way, decided to kill himself and take the blame to protect his sister.
WMG / The Murder of Roger Ackroyd