I actually disagree with this, although I do think it is a possible interpretation.

But I think when you're responding to feedback, one thing that people do that is legitimate is to run through the feedback they've gotten from other people. Several weeks ago a friend of mine was responding to my point that she was being really critical of her husband's behavior. I don't like him at all but I told her that she can sometimes be over-critical. Her response was, "well other people in my life have said something similar to this, so I should consider that."

I don't think it's blaming someone just to say that the feedback they are sharing isn't something they hear from other people. It's not as if the response means anything more than just what it is. It isn't the equivalent of "you're terribly wrong" or "so, it's your problem then." It's a straightforward response that I think is relevant and provides some kind of meaning in a discussion about whether someone is supportive. It's not definitively client-blaming or evidencing counter-transference. In my opinion.