Sorry, that's just wrong. Stable means stable, be it server or desktop. Testing and Unstable are aptly named by Debian, and that's where you should expect issues to arise.
Thats not quite right. Being stable is subjective. Ubuntu and a TON of distro's are based on Debian Unstable. Does that mean they are unstable because of that?
Debian unstable and testing are a bit more unstable, of course, but they are still good enough for desktop.
Given how often Ubuntu breaks hilariously on dist-upgrades, yes, I would say they are unstable. Though for slightly different reasons than the ones the grandparent poster mentioned.