If your iguana knocked your lamp over, you would be covered. It's an accident - that's what insurance is for. Fire is always covered.
Damage by wildlife is in no way covered. If you have an attic full of racoons, you're screwed.
As for public insurance being cheaper, this is a misconception. Public insurance is actually more expensive, just not on the surface. Who do you think pays the thousands of government employees to run organizations like the ICBC (Insurance Corp. of BC - government insurance) You pay those employees via provincial taxes. Same goes for the other operating expenses. The only thing that your premiums pay for in a public system is claims. On top of that, payout and benefits from public insurance are substantially less.
Also, I'm not sure how long ago you moved to Ontario, but over the last couple years, the price of insurance from the public sector has risen steeply. They have realized that their product was underpriced and now are under-reserved. (Reserves are money set aside for potential payouts. When you file a claim, the insurance company will set reserves, effectively locking up that money. As new info comes in [medical reports, repair estimates, etc...], the reserves are adjusted accordingly. This is to ensure the company can afford to pay all their claimants)
Honestly, there is no way I can explain it in this forum. If you truly are interested, check out the "Fraser Institute Report". In the article, there is a link to the full report. You seem like a pretty smart guy. I'm sure you'll have no trouble following it. I will post the link again.