What you’ve learned is partially incorrect and therefore completely dangerous.
You can have the same song/cue in more than one non-exclusive library, with a caveat (below). For example, you could have the same music in Audiosparx, Jingle Punks and Music Dealers.
***OR***
You can sign a song to a single exclusive, and that same composition, under the same or a different name, CANNOT be signed to any other exclusive or non-exclusive. If you do so, you will be in breach of contract. If you sign a song to Killer Tracks for example, you CANNOT sign that song to any other library. Period.
(The caveat from above is that some non-exclusives will prohibit you from placing a cue that is with them into certain other lowball/bargain barrel libraries. Check each non-exclusive for their specific policy on that.)