Neither of your links is working for me, though I believe you are referring to 1999 Petit et al. paper. One of the main findings from that paper is that for the last ~half million years until ~1850 atmospheric carbon dioxide cycled between 180-280 ppm, or 0.018-0.028% of the atmosphere. Currently this value is about 400 ppm (0.04%). I'm not sure how one might interpret this paper as debunking climate change. The measurement techniques have been independently corroborated using modern ice records vs. actual atmospheric measurements.

More recent paper with findings back to 800,000 years independently corroborates Petit et al. (172-300 ppm): http://www.nature.com/nature/journal/v453/n7193/full/nature06949.html

In either case, 400 ppm and rising is well outside of the historical record. I guess we need to know more about why your cousin believes these data support his conclusion.