Regarding the board, there's 2 spots for the pcie connectors. Only one of them is populated, the bottom-right. Top right may have been populated, but it's not likely--there's merely some solder on 1 of the traces, with 2 of them having just a smidge. The 3 areas with burn/fingerprint marks appear to be test points, or otherwise not primary power points.

If they're fingerprints, it's a very high coincidence for them to be sitting right over those pads. Instead it's possible that the reflow oven they used didn't put any solder there, and they used an iron at far too high of a temp to do so by hand. Or it's smudges, or it's something else, but those traces don't appear damaged so there'd be no point for the PCB to be burned there.

Further support for the high-temp hand-hack job is in the bottom-right pcie connector, look at the burnt flux. A clean, proper-temperature flow will not exhibit that.

I do think it's very likely this is a board they've used heavily over the past month--remember, they had at least one of these assembled at the beginning of October, and since then claim to have been trying to get everything running right. For analytical purposes, it should be noted that one board shouldn't be taken by default to represent their whole batch.