"I can’t help thinking that one cancels out the other. If everyone, Q, an independent Thomas, Mark, Matthew, Luke all have this same material, who is embarrassed about it? The multiple attestation is itself an argument against embarrassment" (W. J. Lyons, “A Prophet Is Rejected in His Home Town (Mark 6.4 and Parallels): A Study in the Methodological (In)Consistency of the Jesus Seminar”, JSHJ 6 (2008): 59-84 (79).It turns out that it's something I once said here on the NT Blog while I was reflecting on an SBL session that used the criteria of multiple attestation and embarrassment side by side. I am grateful to John for drawing attention to the passing comment (and, incidentally, for his article, which is an excellent discussion of the problems with the way that the Jesus seminar uses Historical Jesus criteria) because I think there may be something in it.
What other area of the humanities would manage to come up with something so counter-intuitive as criteria that apparently contradict one another? When we are embarrassed about something, do we keep repeating the information? If members of the early church were seriously embarrassed about John's baptism of Jesus, for example, why did they keep repeating it, even celebrating it? Would multiple witnesses really begin their accounts of the "good news" by trumpeting something they all found embarrassing?
If a tradition is multiply attested, it is a tradition that on some level the evangelists were proud to repeat. When they were embarrassed about things, they could easily omit them.