I found a solution that, while unsatisfactory, allows for music to exist on the PRS-650 without any rescan problems. Unfortunately, it requires a memory card containing the music files to be inserted into the Reader.
I find this quite odd when I considered that the PRS-650 comes with a couple tracks on the internal flash storage by default.
I shall look into this further while giving the PRS-650 a proper shakedown since I haven't even begun to test all of its abilities entirely.
Anyone try putting any music files on their PRS-650 and wound up with the same problem?