I'm not the only one who has a problem with this being mislabeled. Why hasn't it been changed?

Yes, you are both correct -> the original title for the VHS release is indeed "Silent Night Deadly Night 4: Initiation":

https://www.youtube.com/watch?v=iRadWkVc-Lc
http://hmnpodcast.com/episode-152-silent-night-deadly-night-part-4-initiation-1990
https://www.newspapers.com/image/?clipping_id=22376330&fcfToken=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJmcmVlLXZpZXctaWQiOjc4MDEwNDc0LCJpYXQiOjE1NjQ5NTg2NDQsImV4cCI6MTU2NTA0NTA0NH0.zzipFKdNY_uPV-AZrIMFThx2DmLgQlejUr06mVmYsd8

The only question is -> with comma or without? I chose for the original title without, and put the other one into the alternative section.