Official comment
If you export the database on computer A then import it on computer B, it takes a relative path into account, discarding the user portion of the file path. If you were to also include your music in that export / import, it would then associate the new computer's music location to the songs in the database.
If you're trying to use an export device to transfer playlists, you can do so by right-clicking on the export playlist on computer B and selecting Import Playlist. Then you can also save the files, no monkeying around with paths is necessary.