i believe that where you pay more, they take the time to cut straight.
if the crossgrain is offgrain and the fabric is ripped in that direction, the rip will also be offgrain. there is nothing that you can ever do to permanently make it square. even if you pull and tug and press it into somewhere-near-true, it will not stay there.
if the rip is offgrain and you fold the fabric selvedge to selvedge, you will have 'ears' sticking out on both ends, which are not doubled and not usable. those will have to be trimmed away. that represents whole inches on each end. on the other hand, if the fabric is offgrain and is cut straight across, there it is. already cut straight with no 'ears'. in either case, if you plan to wash it before you cut, do something to keep the edges from fraying or you'll lose inches anyway. everyone has their favorite method and mine is to sew the two raw edges together, while the fabric is still folded lengthwise, to make a tube. i stay as close to the edge as possible and use a zigzag stitch.
i really hope this helps explain the offgrain question.
EDIT: within the last 25 years i can count on one hand the number of times i have gotten true-grain fabric regardless of price. including upholstery or other home dec or garment fabric. now that most fabrics are being made out-of-country (even by famous mills) this problem has gotten worse.