What if the cloud service that possesses one of the 3 private keys conspires with the bank/vault that possess also one of the 3 private keys?
They would then have two of the three required private keys and could decide to steal your coins, no? Maybe I am missing something here...
Do we have to rely on the fact that the vault is safe and secure and audited and will not conspire with the case cloud services, being independent/separate from them?
If you allow the third key (recovery key) to be kept at Third Key Solutions then yes, you have to trust there will be no conspiracy. Your option during first time setup of your Case would be to store the third key yourself.