It may alter the patch of the scratch as it relates to light reflection afterwards, but if there is a contaminant on the surface or in the nap of whatever you're using, it doesn't matter if you rub one direction or the other, you're going to scuff the surface. If you rub in circles, you get circles. If you rub in lines you'll eventually get lines. It all matters if there are contaminants in your cloth. There is theory to the straight line argument- circles will appear faster because with a circular motion, the contaminants are being rolled in the nap and given more chances to scratch. This is why MF towels are good, they "hug" the contaminants in the nap better. But, my contention with the post was the comment that the key to
avoiding swirls was to not make circles. The key is to avoid swirls is to avoid surface contaminants that will scratch the surface no matter what direction your mitts are moving. But nothing will eliminate them for a daily driver.
The sad thing is that you can be religious about keeping the surface clean and contaminant free, but one lapse after a car wash or trying to dry-wipe a seemingly dust free car can result in swirls that look like they've been building up for years.
You've got to be careful when rubbing any painted surface. I inspect every MF after cleaning to be sure I can't see anything in the nap. I use approx 15-20 MF's when I wax any vehicle, whether mine or a customer- and i still see them eventually. Nothing is 100% foolproof.