I cut sashing strips across the grain for the reason you give -- they are short.
Whenever possible, I like to cut borders along the lengthwise grain because that grain is more stable. It's not the width of the border that makes this desirable so much as it is the length of the border; there is more chance for distortion in a longer length.
Also, strength really isn't the issue with cutting crossgrain vs lengthwise grain. It is the stretchiness of the grain. Crossgrain stretches more than lengthwise grain.
I think all of this holds true no matter what method of quilting is used.