I don't know of Allstate having any insurance policies like that. I use Allstate to insure the companies I own and manage and every time we've had issues I've had to pay first, usually putting a sizable down payment on services rendered and they'd cover what they felt was appropriate to cover and I'd be on the hook for the rest until I hit my maximum, and then they'd cover it IF they felt it was an expense that was outside of my (or my company's) control.
While I haven't been sued directly I've dealt with some seriously dumb shit including attempted sabotages (one more recently) and it's been a nightmare getting them to help even though I've got a great team on their end and an attorney who works with them directly on my behalf.
I think they're both bullshitting about the insurance, and if there is someone paying their bills to that extent, it's not an insurance company.