As Prism99 says,
Ripping/tearing the fabric DOES do damage to the adjacent sides of the tear. I have seen ripples/damage over two inches on each side of the tear - and some the damage is only obvious for a half inch or so on each side.
If a straight of grain cut is important to you - but you need to be miserly with your fabric, the pulled thread method is "safer" - even though a lot more tedious to do.