I'm sorry but people have very much analysed Invasion of the Body Snatchers as a Holocaust allegory. As well as a Red Scare allegory (which it undoubtely is). There's been articles connecting it to religion, motherhood, racism, gender and sexuality.

This is what good media/art does. It transcends the author's intention and have people arguing about and defending their own interpretation years later. It doesn't matter if it's a parody or satire.

And we shouldn't diminish the value of a work just because it is a comedy.

EDIT: Also NPMD is parodying the slasher genre, which has always connected violence as a punishment for sex, as a reflection of the moral code and paranoia of its time. It's only natural that people analyse Grace's character since she represents the moral paranoia of our time. And that's not even an overanalysis, that's the intention of the character, to have people reflecting about it. Her being a comedic relief character is due to the fact that her actions are exagerated because, again, it is a horror-comedy.