Hey, I know I'm coming to this conversation late, but could it be that it is a geocache from a site that is not GC.com? I know I like to do some geocaching games hosted on gpsgames.org and there are others out there.
Some other sites do not have rules against mobile caches, you can place a cache in a spot of significance to you without having to move it 500' from an existing cache, you can do a virtual, there are a number of reasons people use other sites for geocaching. You probably just stumbled upon a cache from one of those.
It is surprising, though, that there was nothing from the cache placer indicating how to log the cache.