I'm not going to back the statistical agruments (because you can't, as you noted), but are you telling me that the fact that 16 of our forum members (or whatever the number currently is) have had to send back their 360s, sometimes multiple times, isn't a potential cause for concern?
Sure it's a potential cause for concern, but not on a scale any bigger than GT.
If we were wanted to start making hypotheses about the data acquired, I think "the XBox360 is prone to a 30% failure rate" is one of the shakiest we could make. It's not out of the realm of possibility, but we've seen no hard evidence that supports that claim yet, just anecdotal evidence.
There are a crapton of hidden variable problems with our self-selected poll that prevent the results from being able to be applied on a product-wide scale. A few notable ones:
1.) Disaffecteds are more likely to report than people who don't have a problem.
2.) We're on a gaming site, so it stands to reason the individuals who responded use their systems for longer periods of time than the average user, and/or used more features of the systems, which meant more of the architecture was exposed to error.
3.) We know nothing about the conditions the systems were kept or used in. In a truly random sampling, that wouldn't matter.
As I've stated above, the evidence I've seen on here and other sites does not suggest the 360 is poorly constructed as much as it suggests the 360 is just as sensitive, if not more so, than a top-of-the-line computer or laptop.
I would argue that you're seeing high failure rates on gaming sites because of the self-selective process. A 'casual' user (3-4 hours a week, let's say) who keeps the 360 in less than optimal conditions, (poor ventilation, dusty/dirty, etc), is going to have his system survive longer than the 'hardcore' user (10+ hours a week, let's say). The common thread between the two is that the system is in less than optimal conditions. A system that has 72 hours to cool off between uses is going to survive shitty conditions, while a system that has less than 24 might not.
The fact that refurb units keep failing can mean any number of things. Maybe MS's refurb process sucks. Maybe the systems are too sensitive to make refurbs even viable. Or maybe the user who gets a refurb which works just fine is still abusing the console in a way that causes failure.
At this point, we just don't know. 30% failure rate is ridiculous, though. That's 1.5 MILLION bad units shipped. Does anyone honestly think that's the case?