Tearing does give you an on grain edge, but your fabric might still look skewed, a trapezoid rather than a rectangle. Don't worry, just grab the two short edges and tug it firmly along the bias, most times this will fix the problem, you may have to do it twice however. To see if it is good fold the fabric length wise, selvage to selvage and see if it lines up OK. I don't worry about the fringe on the torn edge, give it a good press and use your rotary cutter to sliver cut off the threads. You can then rotary cut without problems. I do use tearing on backing as it is a much easier way to deal with large pieces. Since I am going to want my backing to be at least 3" bigger all round I find this works well.