The toads' grisly deaths are, in fact, a well-documented phenomenon.
First recorded in Germany in 1968, exploding toads have been reported
in the country, as well as in Belgium, Denmark and America. Hamburg's
toads started to explode during their week-long mating season. Dr
Mutschmann believes the crows went in for the kill when the toads were
too busy enjoying the heights of sexual excitement. "They would have
noticed something as the crow pecked at them, but it wouldn't have
been particularly painful," he said.
Toads puff up with air as a defense - it makes them scary and also hard to swallow. If a crow has eaten your liver and left a hole but you did not notice at the time, and then you try to puff up, you will explode.
Maybe sometimes toads explode without crow help. If you are overenthusiastic with this particular defense and take it too far, you could pop. If you are full of poison that might spread it around. Taking one for the team in this way would be helpful for your siblings, who would then be avoided by any predator involved in the exploding.