When the story rolled around the first time, people did indeed make the argument that the payment itself was illegal.
The campaign finance laws require expenditures that help your electoral chances to be declared as campaign expenditures.
They also prohibit declaring any expenditures that help you in your personal life.
This leads to the obviously terrible result that while you're campaigning for office, it's illegal to pay for anything that simultaneously helps you electorally ("the voters will never hear about my affair with a stripper!") and in your personal life ("my wife will never hear about my affair with a stripper!"). If you don't declare the campaign expense, you're violating the disclosure laws. If you do declare it, you're embezzling from the campaign.
