cosmic rays graphic
From the paper in PNAS:(h/t to Dr. Leif Svalgaard)
Our results suggest weak to moderate coupling between CR and year-to-year changes of GT," they write. "However, we find that the realized effect is modest at best, and only recoverable when the secular trend in GT is removed." This "secular trend" is the warming widely believed to be caused by excess carbon in the atmosphere, an effect the researchers accounted for by first-differencing. "We show specifically that CR cannot explain secular warming, a trend that the consensus attributes to anthropogenic forcing. Nonetheless, the results verify the presence of a nontraditional forcing in the climate system, an effect that represents another interesting piece of the puzzle in our understanding of factors influencing climate variability,
While they might simply be trading one effect for another with that sort of language, or they might simply be latching on the to Forbush decrease signal, it seems to me that they set out to prove that CR's aren't affecting trend. The fact that they show a link at suggests there's at least some merit to Svenmark's cosmic ray theory.

Significance
Here we use newly available methods to examine the dynamical association between cosmic rays (CR) and global temperature (GT) in the 20th-century observational record. We find no measurable evidence of a causal effect linking CR to the overall 20th-century warming trend; however, on short interannual timescales, we find a significant, although modest, causal effect of CR on short-term, year-to-year variability in GT. Thus, although CR clearly do not contribute measurably to the 20th-century global warming trend, they do appear as a nontraditional forcing in the climate system on short interannual timescales, providing another interesting piece of the puzzle in our understanding of factors influencing climate variability.
Dynamical evidence for causality between galactic cosmic rays and interannual variation in global temperature
  1. Anastasios A. Tsonis
  2. Ethan R. Deyle
  3. Robert M. May
  4. George Sugihara
  5. Kyle Swanson
  6. Joshua D. Verbeten
  7. Geli Wangd
Abstract
As early as 1959, it was hypothesized that an indirect link between solar activity and climate could be mediated by mechanisms controlling the flux of galactic cosmic rays (CR) [Ney ER (1959) Nature 183:451 - 452]. Although the connection between CR and climate remains controversial, a significant body of laboratory evidence has emerged at the European Organization for Nuclear Research [Duplissy J, et al. (2010) Atmos Chem Phys 10:1635 - 1647; Kirkby J, et al. (2011) Nature 476(7361):429 - 433] and elsewhere [Svensmark H, Pedersen JOP, Marsh ND, Enghoff MB, Uggerhøj UI (2007) Proc R Soc A 463:385 - 396; Enghoff MB, Pedersen JOP, Uggerhoj UI, Paling SM, Svensmark H (2011) Geophys Res Lett 38:L09805], demonstrating the theoretical mechanism of this link. In this article, we present an analysis based on convergent cross mapping, which uses observational time series data to directly examine the causal link between CR and year-to-year changes in global temperature. Despite a gross correlation, we find no measurable evidence of a causal effect linking CR to the overall 20th-century warming trend. However, on short interannual timescales, we find a significant, although modest, causal effect between CR and short-term, year-to-year variability in global temperature that is consistent with the presence of nonlinearities internal to the system. Thus, although CR do not contribute measurably to the 20th-century global warming trend, they do appear as a nontraditional forcing in the climate system on short interannual timescales.
The full paper is available here (PDF)