Given the broken spokes the stick hypothesis sounds likely. There is however another common way of breaking off a valve stem. The tire and tube start moving on the rim. Only happens when tire pressure is very low. Happens to those who lube the tube and tire with talc for easier tire mounting. Could happen with a slow leak. Depends a lot on how tight the tire fits. Never happens with a tire inflated hard.
Here’s the part with the nut. If there is no nut the valve stem gets cocked sideways. Hopefully you see that. Then you deflate and realign. And try to remember to keep your tires well inflated. With a nut on there the tube is just as stressed but there is nothing to see. The nut keeps the valve pointed straight. The break comes as a complete surprise.
Stuff happens. I ran over a strip of scrap metal, it wedged between chainring and chain, broke the chain, scarred two chainring teeth. A friend kicked up a stone that hit the frame (steel) so hard the tube dented. Doubt that either of us will ever repeat those incidents. You could ride a lifetime and never have a problem. But it happens.