Was Bates' return ticket found in his coat used or not? There were two triangular punches, one on each half. I assumed that meant that a conductor had punched each half, once on each trip. But the characters talked about the ticket being ripped or torn. If it had to be torn to be used, then the ticket Mary burned was NOT used, and Bates told Anna the truth. But of tickets could be punched, then Bates liked to Anna.
I have another theory. That Green has a history of misdeeds know by Gillingham. Gillingham confronts Green and fires him and threatens to expose him somehow, and Green kills himself. Pretty speculative. I heard the "Mary did it" theory, but it it not her style, and she seemed to feel exposing Bates was the right thing, which she would not do if she knew he did not commit the crime.