No, John doesn't eat Neanderthals.
In a strange instance of dietary synchronicity, given that Atkins is going bankrupt, Hawks gets exasperated with attempts to figure out the heavily carnivorous Neanderthals diet. A number of studies have measured bone collagen nitrogen-15, a heavy isotope which gets enriched as you go up the food chain (but, as Hawks points out, maybe not in a simple way). A study to be published soon reports very high N-15 values in Neanderthal remains, and concludes that Neanderthals ate big beasties--rhinos and mammoth-- compared to horse-eating hyenas.
What's clear is Neanderthals have higher N-15 than contemporaneous hyenas, and it's thought on other grounds that Neanderthals ate up to 95% meat. The high isotope values are remarkable, and consistent with high N-15 found in mammoth of the same epoch. However, mammoth bones are not found in Neanderthal sites. Moreover, bones of Homo Sapiens peoples known to have relied on seafood (the South Beach diet?) give even higher N-15 values. Basically, Hawks thinks you can't conclude much about diet without more data than carbon and nitrogen isotopes.