It's awfully convenient because there hasn't been much paleopathology done on Spartan remains that I can track down. Without study of those remains it's hard to tell what their health was actually like. Were they powerful warriors when they were young, but died bent and toothless? Who knows.
I know one thing that people miss in the Mediterranean diet is the importance of fasting in traditional Greek culture. The monks on Mount Athos fast a lot. They are also close to vegan, but not totally, since they eat mollusks. Overall, they have an ascetic life of prayer and community, which probably counts for some health. They also typically don't go there until they are older, so they aren't eating this diet their entire life.
Occasionally I've come across that blog, but the author doesn't seem to have the greatest grasp of science or stats. The diet he/she is promoting is like the fat-phobic version of WAPF.