This is a common belief, but not true anymore. Emergency rooms have a little vice that can press the ring and gently crack it similarly to what happened to OP’s ring. This means they can be easier to remove than a metal ring which must be cut. I think the way they remove tungsten rings is to apply pressure with vice grips until it cracks (basically like it’s just done in the picture).
My son was learning about metals at some point at school. Tungsten was one of them. Not thinking, I wanted to demonstrate that tungsten was one of the hardest metals, forgetting that that also made it brittle. I threw it on the tile floor and ended up with thousands of pieces all over the kitchen. Well, that sucked.