I don't think I would worry about what a psychiatrist thinks about your school choices. He doesn't even know what "kids like your son" might be, having never met him, and chances are he has never met any kids like your son.
Grade skips in online school are not at all the same thing as grade skips in a regular school, as far as having to be concerned about social matters -- which is probably where the psychiatrist's experience, if any, lies. In traditional school, you're having to think about age differences and behavior and physical limitations of the buildings and schedules -- can the kid get to the advanced classes in a different building, is it at the right time so he's not missing something else, etc. Online, you can choose the classes you need and not worry about the rest -- you have lots of opportunities for the social stuff outside of the online classes.
It sounds to me like you're doing just fine and have everything under control. I would forget about the shrink and just keep taking care of the kid.
