They're different caches, server side. You can clear your cache until Hell freezes over, it won't change a thing. The server side caches are automatically updated at different intervals, IIRC. Cache is only manually cleared if the updates are stuck.
Actually, the page count is part of the page cache which can be cleared by purging the page. However, that would need to be done individually for every page. It is far easier to just wait for the page caches to update automatically.