IMO it's better to think of a directory as "containing" only the named references to inodes. Other directories on the same filesystem may contain other named references to the same inodes ("hard links").

The inodes themselves are more like free floating anonymous objects independent of any particular directory, and might not have a named reference at all (O_TMPFILE; or the named reference was deleted but a file descriptor is still open; or orphaned inodes due to filesystem corruption or someone forgetting to fsync the directory after creating a file as masklinn pointed out - e2fsck will link these in /lost+found). This is also why chmod appears to affect other hard links in different directories: Because it actually modifies the inode (file permissions are recorded in that), not the named reference.