We also have found *lots* of times these darker lines in fabrics. Being nearsighted, I've seen that most of the time it is a single dark fiber (often it feels like something synthetic), spun into the thread and then woven into the cloth. So IMHO the fault is in the weaving mill that makes the greige goods. The various manufacturers probably buy differing qualities of greige goods, and (being the buyer) I am quite vigilant as to which manufacturers are printing on the better cloth, and when shopping for light colors I *only* buy those brands.
If you are looking for a plain solid white... go for Kona. NEVER go for Springs. They have lines all over their light color fabrics, and for some odd reason they are usually red ones. When Moda switched the greige goods for their Marbles about a year ago, we noticed a lot of these lines, and reported it to them. And we stopped buying their light colored Marbles. I'm hoping that they've fixed the problem (they did express concern about it) and next month I will buy a few bolts of their light colors again to check out how they are.
What to do when you find a line? If you are also very nearsighted, you *might* be able to take a fine needle and unwrap the dark fiber from the thread and slowly, slowly get rid of it. About 50% of the time I'm able to do this, the other half of the time I can't fix the problem.