Now you are trying to hold the Landlord responsible for your friend's lack of foresight to get renter's insurance. You also want to imply that the daycare was negligent for doing a fire safety class & not informing the your friend.
At what point does your friend ever take responsibility for her actions or lack thereof? I know when I rented at the age of 18, I had renter's insurance for the contents of my apartment. This was not in my lease, nor should it be. It's just that nowadays some landlords have it in their lease, so that if there is a situation such as your friend's they can be sure to be reimbursed for the damages they suffered. Instead of trying to get a tenant to pay for their responsibility because that can be quite difficult.
Seriously, the landlord did not leave a lighter for her child to play with, your friend did. As for the day care teaching the child fire safety, this should have been done by your friend prior to this time.
Caring for a child is a full time job & a parent has to try to head off any danger a normal person would think of. My child is 19 months old, & incable of operating a lighter or matches, but I keep them well out of his way. At some point a child will express an interest in these items, & is not going to inform the parent beforehand.
To put this another way, most parents try to keep cleaning products, medicines, and other hazardous materials out of a child's reach. (Usually in a high cabinet, or one that has been child proofed.) This is a foreseeable danger (as are matches, lighers, guns, etc.). If a child were to get into these chemicals it would fall under the parent's responsibility, since it is under their control. Would you blame the landlord? The daycare? The company that anufactured the product?
Bottom line, you friend is liable. If she wasn't the insurance company would not waste it's time on such a relatively small claim.