exposure - Why is my camera metering indoor scenes as darker than I expect, forcing me to use a high ISO?

I am shooting in natural light, with my subject facing a full floor-to-ceiling south facing window. You would think my meter would allow ISO between 200-400 in bright light, but I was lucky to get it to 640, with f/3.2 and 1/60 (manual mode).

I've read other places that people say put your ISO down to 100 for indoor shots for greatest clarity (especially sharp eyes) — but don't know how I can with subjects potentially moving. Is there a setting in my camera (Canon 5D Mark III) I am missing, or something that might be making my meter need more light?