I think it is theoretically possible to have limited areas. After all, the intent of the permit is to restrict movement of the local population. Practically, most foreigners will just get a stamp in their passport at the embassy or consulate that says "all areas, except Sarez Lake". I have seen probably a dozen different variations of the stamp. The checkpoint guys often don't know what they are looking at in a foreign passport.
This year I have the separate piece of paper from the OVIR. The areas are handwritten and individually listed. I make a point of not showing it unless specifically being asked. So far so good. As always they ask what country I am from after they study the passport for a while :-) I think they assume as a foreigner you are good to go. Either that, or the "bike talk" distraction works too well.
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