It has been a while since I posted to this. Here is an update. First, thank you to all for your comments. They are greatly appreciated. Second, the insulation is supposed to be creating the vapor barrier (external envelope) of the house since it is in the attic/crawlspace between the kitchen and the roof. Last, I am going ahead with the install by cutting the paper. Since the house is not at all sealed or efficient due to the amateurish job of insulation, I figure what's a few more dollars in energy costs. The difference is between sucks bad or really sucks.

Now, I have a question regarding tiling the backsplash and installing a range hood. I am using some spendy ($20 sq. ft.; the most extravagant thing in the renovation) metal tile from the Blue Store as my backsplash. Would I tile first and then mount the range hood? That would necessitate drilling holes in the tile and covering up a few square feet of it in the process. Or do I make a template of the range hood, mount the range hood and then tile using the template for a cutting guide?

Thanks for the help.