Bank account managers buy funds the same as ordinary investors buy funds. It's just that the bank account manager may give priority to buying in his own bank, and nothing else. There is no restriction on bank account managers to buy funds, and there is no situation that they are not allowed to buy them.
You can buy funds directly from banks or directly from third-party platforms, fund companies and securities companies. Bank account managers can also purchase funds from these channels, as long as they open corresponding accounts.