The answer to who owns the money in a joint account on the death of one of the account holders is "it depends". It depends on a few things: the amount in the account, the reason it was put into joint names, the relationship between the account holders etc.
So for example I manage finances for my v elderly mother and have her accounts in joint names with me so that I can do the necessary for looking after her as she is too old and frail to manage her affairs and pay her bills. When she passes on I will not own the money in the account - and if I tried to claim it my siblings would be extremely unhappy! I should also say that if I asked my Mum now if she wanted me to have it she would probably say "yes". But that would be because she is frail and dependent and I wouldn't dream of relying on it to claim. I just give this as an example.
Another example would be an elderly married couple with all accounts in joint names and no complications like previous partners, litigating children etc. In that case the money - if it were small - would pass to the joint account holder though if it were large the bank would still require probate.
In the case you give it seems right that the family of the deceased would have to give consent unless there is something in writing.