Firstly, a swap is generally traded "on market", i.e at nil market value (the value of the two legs in the swap are the same), so his bank would never have been a billion at risk.

Secondly, banks have unbelievably onerous KYC processes, and he would not have been able to trade with any counterparty that hadn't been through that (there'd be no legal master agreement, no collateral support or margin agreement, no payment authorisation, no way to even book the trade in the banks systems)

So that anecdote is just... bullshit.

(Source: used to be a swap trader at a big bank)