It's not about calling the entire peer review system into question - it's about being skeptical about whether or not results can be trusted on the sole basis they've been peer reviewed - particularly in areas of scientific controversy.
From the linked article: "As Climategate has shown, [the process of peer review] became compromised – causing an instability. As seen in the leaked emails, many within the climate establishment were interrelated and working together to ensure their message of global warming wasn’t diluted. There were even desires to redefine the peer review literature to punish journals that published skeptic’s papers."
It's not just climate science (as I've been reading on nutritional science with Gary Taubes and Robert Lustig).