Bullshit. They break it, they buy you new stuff. Fuck them.
Well, I was exaggerating/being somewhat sarcastic. However, no, most often you have to buy extra insurance on the items, which gets really expensive for a whole house if you want to go with full value protection. Otherwise, it's a paltry reimbursement by weight.
This is pretty standard, so shopping around won't make much of a difference unless you can find a guy willing to work it out in the contract.
You can probably also get some kind of "moving coverage" through your homeowners/renters insurance company, but it's still an extra cost and who actually enjoys the hassle of replacing or getting reimbursed for lost/damaged items?
All I'm saying is if you're trusting a house worth of possessions to a crew, why not give them an incentive to treat your shit kindly.