[S3E9] The Mystery of Bill and Ruth and Phyllis

I am trying to figure out what exactly happened the night that Ruth Davenport was killed, even though I realize that it might not be possible (yet? ever?) to come up with a clear answer.

On the one hand, Bill tells Phyllis, in a seemingly earnest manner, that he was not with Ruth the night that she died but that he dreamed that he had been there. Which leads to conjecture that perhaps he was possessed in some way and killed her.

On the other hand, he tells Tammy that he was with Ruth when she was killed, and it sounds as though she was killed by other unidentified individuals, either Bad Coop/Ray or perhaps Woodsmen. And those people wanted to know his wife's name.

Why the two different stories? And why would the murderers care about Phyllis?