Plumber's digging undermines chimney, who pays for damage?

[Amy A.]

Keep in mind, this all started with a small leak in the basement plumbing of a very old house:

Tenant reported she could hear a leak in the basement when she did laundry.  The leak turned out to be from drain pipes, so we called a plumber to fix it, $1145.  This didn't get to the root of the problem, which was a blockage in the main line.  Called a drain cleaning company.  They found a whole-house trap that the cleaning nozzle couldn't get past.  To get rid of it and clean the whole thing, $1500.  After this, the line was still clogged.  Found another damaged cast iron Y buried in the dirt at the back of the foundation.  They'd have to dig this out and replace it, so the bill went up to $3000 (interestingly, they think the line might continue to serve the back neighbors' property).  

As they were digging to get to the pipe, they undermined the chimney.  The chimney shifted about 4 inches!  There's a big crack in the part going through the living room.  This is now a safety issue.  We'll have to remove the chimney and repair the roof, attic floor, 2nd floor, and kitchen floor and walls.  

I think this should be on the plumbing company's insurance.  They should pay for a new chimney, but we will be fine without it because it wasn't in use anyway.  We just want it safe for the tenants. They say their insurance won't cover it and that ours should cover it.

What do you think?