Hi,
As an xbox 360 owner and an active member of the 360 forums, I can state that this issue is a LOT more widespread than MS would have us beleive.
I am personally on my 4th xbox (well, Ive now had two replaced and bought another one so I have a "backup").
The results of various surveys and postings on the official xbox forums would indicate a failure rate of anything up to 25% over time. and it is NOT just the first batch affected. For example, people are having brand new consoles fail within days.
It is a manufacturing issue, but not restricted to the first batch - the concensus is now starting to lean toward dry joints and brittle solder as the culprit.
Due to new international regulations, the ammount of lead that solder can contain is now lower than ever. Less lead, less flexibility in the solder as it heats/cools. Which means over time, these boxes can just fail due to their natural heating/cooling cycle during use.
Notice how MS are now constructing a new xbox360 with slightly different parts/chips that run cooler? These units may be more stable.
With the failure of an xbox 360 comes other issues too. If you are sent a replacement console, and not your own original one back, any downloaded content will not work offline on your new xbox, you will have to be signed in to xblive for it to work, and it will not work under any other profile on the xbox full stop.
for more on this particular issue - you can read here:
http://forums.xbox.com/1159815/ShowPost.aspx
Hope the above helps,
Regards,
Chris.