Public figure banking is just as insecure as the rest of us' banking services. If thats what you were wondering.
People can and do social engineer wealthy person, celebrity, and public figure banking accounts and can and do steal large sums of money. Sometimes the bank takes the loss, sometimes the celebrity has to jump through a million hoops and ultimately takes the loss themselves never seeing the money again, sometimes the FBI and Secret Service get involved etc.
But it isn't inherently more/less secure, or inherently special. For example, a venture capitalist who ironically invests in technology security solutions recently had $50,000 wired away from his bank account, as the hacker authorized the transfer to the owner's attorney/account using the gmail-trash security flaw. (If you have an email conversation in the trash section of gmail, you won't see notifications of responses. So hackers could be in your gmail account right now talking to various customer support in your trash section, pretending to be you)
The bankers typically know their client's identity. And the current structure of commerce requires having trusted intermediaries that you trust to keep your information confidential. Confidentiality inevitably turns into compromise.
I don't think assistants are able to access their account over phone.
This is not an absolute, there are plenty of ways an assistant can do this and also conceal the identity of the owner of the account.
If a company was used, the assistant could be authorized by the company entity to manage certain aspects of the account. Limited Power of Attorney can also be used for the company account or the individual's account.