I find even if you rip the fabric, down the line you have to true it up again after cutting your strips off of it...now with backing I don't know except I always true up one side so to get it straight with my quilt top. When it is ripped I seem to have this wavy thing going on and don't like it!
I do remember when making garments it is a much bigger piece of fabric to deal with and you do need to know where the exact straight of grain is or your garment will come out twisted when washed after sewing it together. Even so I like a nice even cut, I like to watch very closely to see if it lines up before they cut, if not you can ask them to true it...some will some won't, just happens to be if they want my business or not. Some quilters I understand don't have but one quilt shop around and have to travel miles to get to the nearest one in the first place so must stick with what they do at that shop.