1. Their conclusion is unverifiable. Science is about hypothesis, experiment, and falsification in a reproducible context. When someone says, "I can look at these tree rings and tell you whether rats or marmots spread the plague," I say, "Cool! Show me the results." And when they say, "What do you mean results? I just mean that we infer from the rings to the marmots," then I say, "Okay, well I just infer from planetary alignments to mood swings." Speculation is part of science. Speculation is not science.
2. An extremely strong inference is, by definition, acceptable without further evidence. You don't have to show me an experimental result if you can show me a strong logical case, with very strong causal or inferential links from one piece of evidence to the next. Although you can't reproduce for me a precise result showing that the Grand Canyon was the result of many, many millennia of erosion, you can show me over observable spans of time the general erosion rates in soil of that type with rainfall of that type and I'll accept your inference that many millennia were involved in the Grand Canyon. But tree rings in Asia to disease vectors in Europe? Give me a break.