The problem with jack stand failure isn't the stands themselves failing, but their application. A jack stand needs a stable surface both to sit on and to support. It cannot have lateral pressure being applied or it is more susceptible to tipping over.
Consider the surface. Are you working on concrete (good), asphalt (bad) or dirt/gravel? (Give up, start over). Without a strong solid surface, jack stands will sink into the surface. Even asphalt is soft. Don't believe it? Go out and poke a screw driver into it and tap with a hammer lightly. You'll sink right in. Now imagine a simple jack stand with thin exposed edges for the feet now supporting several tons of pressure. That too will start to sink in, and once you get off balance, the chances of failure increase greatly.
To avoid this, it's not a bad idea to use some plywood or other material to support the stand's footprint over a larger area to prevent it sinking into the surface. This means a level and solid area. If you have soft materials like asphalt or dirt/gravel, plan accordingly with those supports.
I do like the idea of tires or other materials under the vehicle for a backup, but often those can be in the way. Cribbing is another solution.
Look at the jacked up car and ask yourself how many ways can this fail, and what can I do now before it happens to prevent it. That ounce of prevention can prevent tons of crushing death later.
(And that's my 600th post here! Woo!)