First of all, Dean does not run around telling other characters that he's saying "yes" to Michael because of his lack of faith in Sam. It seems very unlikely that he said anything of the sort in the letters he sends to his loved ones, when planning to say yes. He certainly makes no such claim in his confrontation with Sam at the motel. Nor does he blame Sam in his bitter conversation with Bobby. As cynical and mocking as he is in their scene with Adam, he again doesn't give any indication of blaming Sam. It's not until he is alone with Sam in the panic room that the truth comes out.
Even then, it doesn't come out right away. First, there's a whole digression where Dean blames himself and Sam for the deaths of everyone they ever met.
Finally, Sam asks directly why Dean won't stick with him and Bobby and say "no" to Lucifer. We then get this exchange:
Sam: Why not? Dean, seriously. Tell me. I—I want to know.
Dean: I just…I—I don’t believe.
Sam: In what?
Dean: In you.
The interpretation of this as Dean being terrible and mean to Sam reminds me of an argument in Doctor Who fandom. I have always been of the opinion that the Tenth Doctor was awful to Jack Harkness when they were reunited at the end of the 3rd season (of the new series). Even still, I was stunned by some of the complaints I saw against the Doctor in fandom. For example, some fans were appalled by the Doctor telling Jack that he came back "wrong" after Rose resurrected him. I disagree. Here's the thing: Jack had asked a question, asked why the Doctor had abandoned him. The Doctor told him the truth, even though it was not a nice truth, not reassuring to Jack or flattering to the Doctor. Jack then told the Doctor he was bigoted; the Doctor agreed. Sure, it hurt Jack to hear that the Doctor thought he was "wrong". And yes, the Doctor's initial choice to abandon Jack was wrong. But that doesn't mean the Doctor was wrong to give Jack the truth, even if it hurt. I am certain Jack preferred that.
The same with Sam here. He asked for the truth. Even when Sam asked, Dean was hesitant to tell him. Dean didn't tell Sam until Sam really pushed, and then Dean told the truth. Dean didn't want to tell Sam, he didn't want to hurt Sam.
And here's the thing: Not believing in someone is not a choice. Whether one agrees with Dean about Sam or not (and I disagree with his arguments but not his conclusion - remember, Sam does say "yes" to Lucifer), you can't argue with how Dean feels, with what faith he has or doesn't have. Again, Dean did not want to tell Sam how he felt.
Dean only appears in a couple more scenes after this one before he changes his mind about Michael. Still, I think it is worth noting that he does not mention his lack of faith in Sam in those scenes. This is not something he wanted to say to Sam. This is not something he would have said to Sam if Sam had not pushed for the truth.