It's a historical thing: manually generating patches with diff almost always includes one extra level of path because of the way diff is traditionally used (two copies of the source in different directories, one unmodified, one modified), so patch defaults to stripping one.
These days patches are often generated by version control tools like svn, which aren't really comparing directories but revisions, and so often choose not to put that extra level in as it conveys nothing useful. It depends what tool generated the patch, and what options the user generating the patch used, as to whether you need -p0 or -p1. (higher levels are very uncommon).