The bulk of their paper (http://capmag.com/article.asp?ID=478) does not support your claim. Quite simply, they give numerous worldwide examples of warming during the LO and cooling during the LIA.
The link you posted is not a peer-reviewed paper, just an opinion piece. Also, since it was posted 2 years before the paper in question, I have doubts about how relevant it is. It was posted 2 years earlier. However I do note that it still quotes from Keigwin (see my comments re his work on the Sargasso Sea above).
The quote I gave was directly from their methodology. Let me repeat it again.
"Table 1 and Figs. 1 to 3 summarize the answers to the
questions posed here about local climatic anomalies.
For Questions (1) and (2), we answered ‘Yes’ if the
proxy record showed a period longer than 50 yr of
cooling, wetness or dryness during the Little Ice Age,
and similarly for a period of 50 yr or longer for warming,
wetness or dryness during the Medieval Warm
Period."
That is a direct quote from their paper. So are you saying that it is sound methodology to count a period of both wet and dry as an indication of both warming and cooling?