If it were pressure sensitization due to cutting, well, you have 4 cut areas per sheet so by this reasoning you should (or could) have up to 4 black lines per sheet.
When you see only one black line, and can attribute it to a factory problem it may be one of several things:
1. Pressure sensitivity fogging the paper which is set on end as a whole roll. This crushes one edge and can fog it.
2. A light fog along one edge due to some sort of leak at the factory or in packing. Check the black bag and see if the seal is tight along the fogged edge.
I'll probably think of a few more.