I'd LIKE to believe this, but is it real?

Article in "Nature Climate Change" (who ever they may be, I never heard of 'em before) claims that tree ring width measurements from present day back to Roman times show a persistent global cooling has been going on for the last two thousand years.  I'd like to believe this.
   Trouble is, tree ring width is determined by rainfall.  Trees love moisture and on wet years they lay down thicker layers of new wood. Temperature doesn't effect ring growth much. 
  The authors attempt to meet this criticism by comparing tree ring widths to measured temperatures in modern (post-thermometer-invention) times.  They claim a correlation of 0.77 which is better than random, but far short of the standards used in the real sciences.  For instance the Higgs Boson discoverers demanded a correlation of 0.999 or better before they made their claim.  So I am not sold on tree ring width as a proxy measurement of temperature. 
   The title of the article suggests that the temperature changes are a result of  changes in Earth's orbit.  It has been known for hundreds of years that earth's orbit is not a perfect circle, is it a plump elipse, close to a circle but there is a perihelion (closest to the sun point) and aphelion (farthest from the sun point).  The differences are not great, a percent or so.  Plus the earth's axial tilt (which causes seasons) drifts around some, which means some times Northern Hemisphere summer happens at perihelion, giving warmer summers.  Some times Northern summer happens at aphelion giving cooler summers.  The whole effect cycles around with a period of 25,000 years.  The cycle is called the Drayson cycle, it has been known for centuries, and numerous attempts have been made to connect Draysonianism with the coming and going of the ice ages.  None of these attempts have convinced the bulk of the scientific community to believe them.
    The title suggests another attempt at selling Draysonianism as a cause for global cooling is under way.  Trouble is, they don't have the data to make the case.  Their tree-ring/temperature data only covers 2000 years, a Drayson cycle is 25000 years. To show that we have a 25000 year global cooling cycle driven by the 25000 year Drayson cycle, you need 25000 years worth of temperature data, which they don't have.
   So , a nice article, which I want to believe, but  their case is shaky, at best.