We redesigned the core of RadMap (WPF implementation of the MultiScaleImage and MultiScaleTileSource which perform downloading and showing tiles) in the 2012.Q3 release. With this version it should stop reloading tiles when the map provider is unloaded. For example when you change the OSM provider to the Empty provider then RadMap stops downloading tiles from OSM. Also it should stop downloading when you unload the control which contains RadMap. So, I would recommend using the latest version of RadMap.
The OpenStreet map provider works as designed. It randomizes URL of the tile when new tile is requested. But currently the engine does not call GetTile also in case when the downloading of a tile is failed. This feature is not in our plans for Q2 2013 and I am afraid no certain time frame can be given at the moment.
the Telerik team