These two opinions seem to reflect the difference between appearance and reality, and I suspect that they are in there for that purpose. From the external point of view, Chillingworth is a physician and would certainly want to "comfort" Dimmesdale; others "see" the internals of Chillingworth and know that he is not at all intent on helping. I think this question reflects Hawthorne's fascination with the ambiguous nature of most people and situations.
I can only hazard a guess and an opinion about this topic as I am not a Puritan (though I am a Christian). I think this is a difficult one to answer as we are so set in our 21st-century lives that it is difficult to imagine what the Puritans truly believed in their hearts. However, because Chillingworth was so inherently evil...so determined to seek revenge for Dimmesdale's adultery with Hester...I can't help but believe that Chillingworth was sent by Satan. It was never Chillingworth's intent to cure and forgive Dimmesdale - he was there to punish him, and that is not something that God does. God says to leave the punishing and the judgment to him, not to take it into our own hands. I just can't believe that God would have sent Chillingworth to do those things to Dimmesdale...but again, that is my two cents coming from 2008.