I doubt that's the scratch and dent problem. That's the Korean Guitar problem.
Shouldn't the Korean axes go to Line 6 for QC before being shipped to dealers? If so, that could, indeed, be the s&d problem. If, however, L6 isn't QCing the axes before delivery to dealers, that's a major corporate mal-decision.
You might be able to shift the nut or just replace it. Also sight down the neck and make sure the strings are aligned with the edges. I looked at several JTV69's and some had the neck set crooked so the strings were not parallel with the neck. I picked one that was set correctly and my strings don't fall off the neck.
I just sighted the neck, and it is, indeed, just a wee bit crooked (maybe 1/64th off?), but the problem can, I think, be cured with a new nut. I'll be taking it to a luthier I know. I think I want him to narrow the string spacing just a touch, leave the 6th string placement where it is, keep the depth on the 3rd thru 6th strings as they are, but deepen the cuts for the 1st and 2nd strings. That, IMHO, would make this a beautifully-playing guitar.