An idea that I have is that they have formed such a strong association between our skin color and food (since we often, but not always, feed them by hand) that sometimes our skin looks even more enticing than the food we're offering. The problem with this theory is the fact that they will continue to bite a finger for several minutes until they finally give up on the idea of getting any food for all the energy being spent (or they are tired of the salty taste of our skin).
Oddly enough, while Hector and Phoebe bring the total number of Greek Tortoises we have had to five, they are the only two that have ever exhibited this behavior. If any of our past Greek Tortoises ever bit a finger it was on accident while we were feeding them. (A notable exception to this rule occurred with Sampson I as seen here).
They don't even care how big the skin is, they just like to chew on it.