Actually, the narrower the border the more it has the possibility of 'wobbling" and shifting. If I'm cutting a narrow border or long narrow sashing I'll try to cut it lengthwise, even if I have to piece it (pieced narrow borders are less visible than wide narrow borders - especially with prints). Smaller cross sashing I'll cut across the width, ditto if the border is wide. However, if it's a wide printed border I'll try to cut it lengthwise to avoid matching the print in piecing.
I consider a narrow border 3" or less.