The theory seems to be that the lack of minerals in RO water might serve to leech minerals from one's body. I think there's also some concern RO water might leech from cooking vessels and organic compounds in plastic tubing, etc.

I have no idea how real the risk is, and it all seems less risky than drinking unfiltered water in most areas.

But it's no headache for me to mix RO water with bottled spring water, since I prefer the flavor and it takes seconds.