I recognized the quote as something I'd received in my email long ago. It's a pretty funny article, often attributed to Douglas Adams, but
this site, which has the essay, says otherwise.
Yes, it appears a wombat could indeed crush your hand, although perhaps not because it believes its burrow is collapsing-- I reckon it would dig in that case. "Its back is hard and bony. This bony back is a useful defence against intruders in the burrow, as the wombat uses its back to crush them against the burrow wall."
Cite. "Wombats are nocturnal animals and have very poor eyesight. They are perceived as a slow animal and not very dangerous. This however is very wrong as they can cause a nasty bite and are capable of running at a speed of up to 40 klms per hour. If you find one in a burrow, it is wise to leave it undisturbed. Prevent your dogs from going down the burrow as the dog will often come off worse for wear, or may even be killed, as the wombat will crush the dog to the roof of the burrow as a form of self defense."
Cite. As for ways to die in Australia, having your hand crushed in a wombat burrow is indeed the third most embarassing. Unfortunately, Jim was mistaken. Australia has several ways to die that are more embarassing than a bus accident while wearing the wrong undergarment.
The 10 Most Embarassing Ways to Die in Australia
1. Kicked to death by Dame Edna in pub brawl.
2. Alcohol poisoning-- but only if brought on by light beer. Normal cases of alcohol poisoning get a free burial.
3. Hand crushed in wombat burrow.
4. Heart attack due to yelling at the footy on the tellie.
5. 'Roo stampede.
6. Bus accident while wearing inappropiately dirty and/or frilly undies.
7. Losing a knife-fight with a pom.
8. Losing a gun-fight with a seppo.
9. Bursting a blood-vessel trying to hit high notes in an ABBA tune.
10. Magpie attack.
I didn't just make that up. It's from a 1987 poll.
Cite.