As a shop owner, I cut my regular width fabric. I do try and check the bolts to be sure they are wound fairly straight - if not I will straighten the first edge and then adjust when I make cuts from it.
HOWEVER, with wide backing fabric, I ALWAYS tear. I have a post on my blog with photos that will explain why:
http://andicrafts.wordpress.com/2010...ad-of-cutting/
Andi