Well, they can find the CO2 levels
and the actual temperatures by studying the isotopes found in the ice cores (
link explaining the science). Through isotopic analysis, they can determine the atmospheric temperature when the ice froze. They're not extrapolating the temperatures from the CO2 levels, they are looking at the CO2 levels
and the temperatures independently and then noticed a correlation between the two. So yes, it is an accurate record of temperatures. Antarctic is also relatively unspoiled by outside pollutants that might effect the results as well. I think they drilled in several locations too, but I cannot determine that for sure.
Furthermore, their data has been published in reputable journals, scrutinized by the scientific community, and found to be sound. You can laugh at me all you want, but I trust the work of numerous experts working through the scientific method.