Tungsten rings can almost always be removed in an emergency situation. Almost all hospitals and emergency responders carry special tools to remove rings. Tungsten rings are no different to remove than other rings.
Other metal rings can be cut off but tungsten rings can also be safely broken off with a pair of pliers when enough pressure is applied.
Many experts say tungsten rings are safer to wear because they will break/shatter when they come under great amounts of pressure. Versus a solid gold ring which will just bend around the finger.