For lists and libraries, SharePoint locks the URLs to whatever value the name was when the list/library was created. Later, if you rename the list/library, it will reflect the new name everywhere except in the URL.
From your description, it sounds like you are saying the URL.....
.....works, but the library name is really "MY DOCUMENT LIBRARY".
If that is the case, then it means the user named the library "MYDOCUMENTLIBRARY" when they first created it, but they have since renamed to "MY DOCUMENT LIBRARY".
Using this renaming trick is a common 'best practice' since it makes your URLs a bit cleaner as you can avoid the encoded spaces (%20).