You bring up a good issue, and I supose it comes down to a judgement call, influenced by such details as whether the "living room" side doubles as a bar, or if there are lights in the ceiling around or above it.
Kitchen islands and penninsulas present unique challenges to the electrician, and the code doesn't (in my opinion) address them very well.
I believe that the counter-top receptacle requirement is predicated on the assumption that some sort of appliance will be used atop the counter. Where some feature of the design precludes the use of appliances- such as a sink or cooktop- I don't think a receptacle is needed.
Likewise, the "six foot rule" for placing receptacles on the wall.....no point along the floor line being more than six feet from a receptacle.....seems to assume a floor or table lamp with a six foot cord.
With that in mind, a penninsula almost seems to be a traffic area, much like a hall or a doorway, and I don't thing a receptacle would be needed.
If you are placing a receptacle for this reason, then you are not "using" it to serve the counter, and it would not have to be within 12" of the top. Likewise, a receptacle more than 12" below the top would not qualify as a required receptacle for the top.