Note, blue carries on upwards, while red shoots downwards. Bang goes that lousy theory.
Your solar fanatic might say we don't need them any more, but they were, none-the-less, a reality, something that happened that had a significant impact on global temperatures. After all, those lost decades have been brought up enough in attempts to attack the role of CO2 as a climate forcer.
But to preserve the correlation, you have to assume those emissions had NO EFFECT - whereas we know they do. Witness Pinatubo blasting off in 1991. So the sun spot cycle 'correlation' relies on excluding not one, but two massive climate influences - particulate emissions and increasing CO2 concentrations - that have affected global temperature over decades.
So, nonsense, really. When something looks too good to be true ...
1 - The graph originates in the work of Egil Friis-Christensen and Knud Lassen, originally published in "Length of the Solar Cycle: An Indicator of Solar Activity Closely Associated with Climate," in Science, issue 254, in 1991. I can not say who has since added the pretty colours and the CO2 levels to the original work. I found the version reproduced above here, "10 Questions for Climate Fascists," posted by Jack Lacton, on Kerplunk - Common sense from Down Under, 14th of March, 2007. (http://ker-plunk.blogspot.com/2007/03/kerplunk-list-of-climate-fascists.html)
2 - The updated version of the graph was borrowed from "Sun Activity Does Correlate with Temperature," unattributed work posted on Friends of Science, (http://members.shaw.ca/sch25/FOS/Climate_Change_Science.html#Sun_Activity). While I don't know the state of the arthmetic underpinning this version, given the generally sceptical slant of the website, I'm willing to run with it for now.