Based on your description, it sounds like the guy was trying to blame the "Mexican batteries" and I have to say that I seriously doubt if that was the case. Being an Olympus, it probably takes AA batteries (or something similar) and really...a AA battery is a AA battery regardless of what country you're in. I find it -very- unlikely that a AA battery could have caused enough of a voltage surge to cause the problems your describing. Unfortunately any of a 100 other things could have caused this problem.
You said "he swears he didn't drop it" but if he was on vacation or something, perhaps someone else did...the kids, his wife, etc.. Picture this, the guy decides to go to the beach for the afternoon and leaves the camera in the hotel room so that it doesn't get wet at the beach. The maid comes in to the clean the room and knocks the camera off the table...looks around to see if anyone saw it, then quietly picks the camera back up and puts it back on the table. No the guy didn't drop it...doesn't mean someone else didn't when he wasn't watching. Maybe he was a business man on a company trip and at one point after his corporate meeting, he stuffed it in his briefcase and slammed the thing closed. Maybe it got jostled around in his luggage and it just took a day or two for the camera to start acting up.
Also being in Mexico, depending on where he was it could also have been something like heat or humidity. Since you said it was a "pocket size" Olympus, I have to say that most p&s cameras don't always hold up very well to adverse conditions. If the conditions are severe enough, even high priced DSLR's can have problems (the joy of the electronic age). Maybe the guy left it on the dashboard of a car (or tour bus) or something and while the heat wasn't enough to melt the case of the camera, maybe one of the pc boards inside the camera got hot enough to warp a little and crack a circuit or contact. For that matter, maybe he kept it in his pocket the whole time and the same thing happened or maybe he was sweating his butt off in that Mexican heat with the camera in his pocket and some condensation formed inside the camera causing something to short. Maybe the guy did take it to the beach and someone splashed it without his realizing it. Maybe at one point since the batteries had gone dead, the guy tried to use an international power adapter of some kind to plug it in in his hotel room and whooooooosh...wrong voltage (or the adapter had the polarity reversed). Perhaps someone at the airport banged it really good going thru customs and it just took a day or two for the camera to start acting up. It's even possible that it could have simply been a manufacturers defect that just waited until that moment to rear it's ugly little head. Like I said...any of a 100 things could have happened without the guy even realizing it. Maybe the guy even dropped it himself or something and just doesn't want to admit it for fear of being called a dumba@@...it's been my experience that most people really don't like to accept responsibility for their own actions (people like to jump up and down yelling "It's not my fault! It's not my fault!" and now a days, it don't mean crap).
If you see the guy again, the logical course of action is that if the camera is still under warranty, send it in and see what Olympus has to say. But be warned...most warranties only really cover those manufacturer defects. If something did actually happen to the camera such as a power surge or it being dropped when the guy didn't see it, etc., that probably won't be covered....and believe me...they can usually tell. Most warranties don't usually have a "stupidity clause". If that's the case, the guy could probably pay for the repair but depending on the model of the camera, it just may be easier (and/or cheaper) for him to simply buy a new one. If the camera isn't under warranty, honestly...I wouldn't even bother sending it in. If it were a high priced DSLR or something yea, it'd be worth it, but for a cheapy p&s? The repair and shipping costs would probably be close to, if not more than the camera is worth. Buy a new one and sell the old one on Ebay for $20 as parts.
Lastly, -if- the camera is NOT under warranty and if it's going on Ebay or in the trash anyways, I'd also suggest maybe crack the sucker open and take a quick look-see. On many digital cameras, those LCD's are often connected via a tiny ribbon cable with these tiny little connectors (in some ways it's amazing that they even work to begin with! LOL!). Since you said the camera was otherwise working fine, it's possible that maybe the ribbon cable came out of the connector or something relatively easy to fix. In the case of my Sony H1, I had actually dumped coffee on it during a trip down to Kentucky last year...actually hit a chuck hole and the coffee cup jumped off the dashboard and landed smack dab on the camera. By the time we got back home, the coffee (with the extra sugar and cream) had pretty much glued all the controls solid...I couldn't even press the power button. I knew this was not something that Sony would honor under warranty (nor should they), so I just went ahead, took the covers off and cleaned it with a few Q-tips and rubbing alcohol...camera was good as new afterwards (and still works to this day!). The point is, if the camera is trash anyways, it never hurts to crack it open and take a look.
I'm sure that probably wasn't much help, but there it is...