What type of commercial STR insurance policy do they carry (above and beyond insurance provided by the likes of Airbnb) in the event of any accidents, injuries, or damage to the property? 

There are certainly some advantages to holding flips in a business entity when it comes to liability, particularly for personal injury or wrongful death. 

I don't even leave snorkels for my guests to use for fear of injury - having a car that needs something I'm not aware of is just asking for trouble.Now, if you are a motorhead, live nearby, etc, that's a different story IMO.

The insurance doesn't have a vicious dog list but they don't cover any damage/injury made by tenants' dogs.

Owner agrees to pay Manager’s attorney's fees related to Manager’s management of the herein-described property and any liability for injury on or about the property which may be suffered by any employee, Tenant or guest upon the property.

If there is a fire and there is an injury there will be a lawsuit. 

You would not hire a yard service if they did not have coverage for damage/injury from a normal piece of yard maintenance equipment.

I think where there is confusion is the agent seems to imply if they are working on the vehicle, there wouldn't be liability coverage if something should happen like an injury, but maybe this is my misunderstanding.

Most likely the state where the property is located is where lawsuits would be brought if they are something for personal injury like a trip and fall or something of that nature because the “cause of action” arose in that state.

Their are multiple tradeoffs for each positions, but the big ones are: Anti Registration: The rental stock will be more prone to having dangerous code violations, which in turn, on average will increase the rate of injury and death.