Hopefully OP will comment on their final result. However if my car needed an engine replacement, I had that offer from the manufacturer @Askitiki , I’d take it. Worse case you spend $500 and they determine the problem was caused by running the engine with low oil or engine overheated, so they won’t replace the engine. But pretty good chance the $500 test will show the engine failed b/c of known design/manufacturing problems, and then they’ll install a replacement engine for you gratis. Seems like a pretty generous offer, good on Hyundai, means they value their customers.
I would pay the $500 and see what, if anything, Hyundai offers. If the answer is “nothing at all”, then you can tow the vehicle elsewhere to have the engine repaired or replaced.
I just worry that they will not be honest even if they do find they are at fault. How would I even know?
Make sure they give you a complete explanation for why the engine failed and compare that to the TSB referenced above. For that price, I’d get a second opinion at another Hyundai or Kia dealer. If another dealer isn’t available, then try a good local indie shop.
Appears to be a stand off. Hyundai is in exactly the same situation. How would they know if the engine was damaged by the negligence of a prior owner, absent an inspection? My guess, the manufacturer’s intension is to be honest & generate customer goodwill, otherwise they wouldn’t have made what seems a pretty generous offer. If you don’t concur with their inspection findings, you always have the option of obtaining (& paying again for) your own independent inspection. If the results of the inspection is it’s a design/manufacturing problem and they will replace the engine, you could argue they should also refund the $500 I suppose.
I don’t know what would be involved for $500 but I would think they would at least pull the pan and chech the bearings for any evidence of oil starvation. Probably at least a compression test and maybe even pull a head or use a scope to check the cylinders. I guess at least it would be nice to know what happened but suspect they have corporate procedure to follow to verify a bad engine.