klach: Even granting that we pasken that way for all pesukim, could you please ask your rebbi why he extends that halacha to a Rashi? The answer would interest me greatly.
Haleivi: The gemara in Sanhedrin refers to singing shir hashirim “in a tavern” i.e. coarsely, removing the holy meaning from the words. That would apply to many songs whose tunes don’t fit the words in any way, merely using them to have something to set to the melody. I’ve been saying that Jewish songwriters should write their own lyrics for a very long time.