I troubleshoot home theater electronics all day, every day. I have to wonder if something else is at work here. At least one person asked, what do these eleven units all have in common? The same working environment. There are plenty of Xbox 360s out there, and they certainly all aren't failures, and the chance that this one person has received every part from the 1-2% of doomed 360s out there that are failures would be nearly statistically impossible.
More likely is that some other factor is causing this, perhaps the powerstrip he's plugged it into has a badly grounded outlet, or perhaps the main outlet itself - or possibly any of another hundred or so electrical issues there could be - such issues tend to plague complex electronics in very odd ways, and not the same way every time.
If I were at Microsoft, I'd replace his unit, but advise this guy he needs to get some help looking for what other factors could be causing these malfunctions.