But for your question, with LEO satellites you don't really target specific countries. They cover every country within a given latitude range. A round LEO orbit that goes over the US must also go over China.

However you don't need geostationary orbits to target a given part of the globe. Molniya orbits do the same thing more or less and work better if you want coverage further away from the equator. They were popularized by the USSR and the US and China use them to varying extents.