Some paper holders are designed specifically for under-hung rolls and others for over-hung rolls.
And just for GneissGuy, there are also full cover flaps available to defeat the family cat.
Dear Abby or Ann Landers had a near civil war several years ago over toilet paper.
Although I live alone, I have a great many people that come thru my house on a regular basis. It's a rare week that someone doesn't reverse my T-P roll!