I think this was exactly the point. You mix a scary part of the trailer (where a girl takes revenge on her attackers) with a cheesy version of a love song about a girl. Kinda cool.
I think this cover fits the movie.
SC's cover of SCOM was bad, imho. That is won a grammy speaks volumes to how little that designation means to me.
The original Last House on the Left is a bit dated. A lot of emphasis on women's lib that was lost on me even 24 years ago when I saw it.