Vertical pixel-thick lines on display

I'm seeing a vertical line on my display. Usually there is just the one, but sometimes more. They are only ever 1 pixel thick but often occur in different places across the screen.

My screen is the high resolution matte version (if that makes any difference).

It's usually a red line that shows best with a darker background. Looking closely at the line it will go from a static straight line to a flickering line, then back.

I've taken the Macbook into an Apple Store and they confirmed that it isn't a problem with the logic board or graphics card as it can output to an external display just fine. I've replaced the LVDS cable but it still shows.

Could it only be the display itself now? I had originally thought it wouldn't be because the line will sometimes shift to another location.