This patent design from 1891 doesn't account for how it should be inserted into the holder. The earliest patent for a rolled toilet paper holder which includes the paper in the diagram (filed in 1891) does indeed demonstrate that it should be rolled over rather than under. It can be seen here: 

https://www.google.com/patents/US469301?dq=rolled+toilet+paper&hl=en&sa=X&ei=lx0HVc7VNMmggwTS2oP4Dg&ved=0CB4Q6AEwAA 

And true to human nature, some a year later, some a-hole patented a roll-under version: 

https://www.google.com/patents/US498900?dq=rolled+toilet+paper&hl=en&sa=X&ei=lx0HVc7VNMmggwTS2oP4Dg&ved=0CCUQ6AEwAQ

Imgur comments: http://imgur.com/lFNstH6

Reddit comments:

http://reddit.com/r/oddlysatisfying/comments/2z8ckl/this_1891_patent_drawing_for_tp_settles_the_over/

It's already been settled.  Over as there should never be a situation where two different people touch the same piece of toilet paper.  Over, and subsequently high end hotels that have toilet paper roll covers, prevents such a situation. 

Isn't high end more like this?

I go by the hotel test too, in nicer hotels it's always over, cheap motels it could be either way.  In homes it could be under, if you have a cat that will roll it out if it's over.

That's the main downside to over: Easier for cats to destroy.