Three Ton Jack Stands : Fail!!
See photo. Just holding up an old Imperial, sort of!
Looking at your photo made me realize that if you don't bend the little retaining tab in, you can potentially engage teeth lower on the cast portion, making the stand taller. Looking at my 6 tons just now, its a difference of almost 3 inches. That would certainly increase bending moment on the cast portion, along with preventing it from properly engaging the throat that makes it stable.
I'm not saying that your stand failed due to that, but I do think I will make sure the tab is bent and/or I make sure not to overextend any stands in the future.
On the other hand, I made wood cribbing out of dimensional lumber screwed together. I use that under a jackstand whenever possible to limit the extension on the saddle. They are way more stable that way.
I also try to throw a tire or leave the floor jack in place. Always like to have a backup plan. I also use 6 ton jackstands on pretty much everything that's going more than 16" off the ground. 12 tons if they get much higher than that. Basically use the widest stand possible for stability.