No. The person who arranges the funeral and contracts with the funeral home is the one responsible for the cost.
That can be true also. But based on the OP's question of a specific person being responsible then until we know more its up for grabs. Funerals are a business and like with any other contract the person doing the buying would be responsible for the bill. But in this case we don't know who did what.
Agreed. I jumped the gun in assuming that, since the question was in seniors, there wasn't an estate and someone was trying to convince Marx2 that the sibling is the responsible party. But, you are right, until we have more info, it is up for grabs.