Most of his income would be within corporations where it is offset by lots of business expenses. He may allow very little income to reach him but his companies and properties would pay all kind of taxes.
As to the statement that most billionaires wouldn’t take the tiny deduction, how many billionaires do they have, did they search all their tax records, and what’s wrong with taking a legal deduction?
The tax preparation and accounting costs far exceed the benefit. (for a billionaire).