The whole process can be described as clusterf$%^k.
Basically when you return a GPU to a store, it will go first to their tech dept. for inspection (if they have this department at all), or maybe to one of their subcontractors. If they think it's a manufacturing defect, it will probably not go to manufacturer directly. It'll first make a stop at the warehouse of that store's supplier (usually a large electronics distributor, which works directly with manufacturer and only sells to large retailers). Depending on how good or bad they are, they may put their final verdict on paper and maybe attempt to fix it. If fix did not help, then you will get a replacement, while your old GPU will spend the next few months or a year in the warehouse, either waiting to be shipped back to OEM, or later written off as "discarded" and sold for pennies to dudes like me. On each stage there are actual specialists with tools and knowledge to fix it, but the main issue is motivation. OEM is not motivated to fix stuff, 'cause their markup on hardware allows to do certain percentage of replacements. Big distributors aren't motivated either, because company has a contract, and their tech dudes are on fixed salary. The only exception is when OEM kicks their ass when their RMA dept. has weird statistics (higher % of defective cards than others, or they are really lazy and put the same diagnosis on all cards without looking at them). And stores aren't motivated to fix it or spend any time on this process, cause it costs them money. A good store will do everything by the book, and it'll take time. A bad store may simply create an excuse to refuse RMA, even if it's not your fault. E.g. they can tell that "the card was mishandled and killed by static electricity", or "your PSU killed it".
Regarding your original question, it's actually quite easy. Visual inspection is step 1. If you see physically damaged or missing components - it's definitely user's fault. If you see liquid damage or corrosion - user's fault 110%, and it's super-easy to spot under UV. If someone unskilled tried to repair or hardmod that card on their own, you can usually spot it even without microscope. If it was baked - there's gonna be some darkened or melted plastic, PCB discoloration and/or crumbling chokes. Wrong BIOS is also one of the things that's spottable, but I don't think anyone checks it during initial inspection.
Then if situation allows, they plug in the card and confirm or disprove user complaints.
And only afterwards, on the last stage of this process, you see poking and prodding with multimeter and oscilloscope, 'cause if it's not user's fault, they still need to put a final diagnosis as to why this GPU is dead and what's broken. Nothing super-fancy, just test for shorts, or maybe probe a few signals, and move on to the next one. Labor costs money, and no one wants to spend a whole day trying to repair some GT1030.