One comment Rudolph W. Giuliani made Sunday has been getting short shrift. In one fell swoop, he offered a false legal argument that both watered down the Trump team’s previous denials and — most important — seemed to admit to the underlying crime.

Speaking with ABC’s George Stephanopoulos, Giuliani sought to argue that Michael Cohen’s hush-money payments made on President Trump’s behalf can’t be campaign finance violations if they served any kind of personal purpose.

“It has to be for the sole purpose,” Giuliani said. “If there’s another purpose, it’s no longer a campaign contribution — if there’s a personal purpose."

He then suggested that the failed prosecution of John Edwards for a campaign finance violation bolstered his point: “It’s not a contribution if it’s intended for a purpose in addition to the campaign purpose. In the case of [Edwards’s lover] Rielle Hunter, right, the payment of $1.1 million was intended to shut her up and was intended to avoid embarrassment with [Edwards’s] wife and with his children.”

The first point is that this is simply not true. The law does not say that a campaign finance violation exists only if the “sole purpose” of it is to affect a campaign. In fact, it says a contribution is “any gift, subscription, loan, advance, or deposit of money or anything of value made by any person for the purpose of influencing any election for Federal office.” This definition doesn’t carve out exceptions for things that were also for personal purposes (indeed, if that were the case, basically nothing would qualify). Instead, it says anything with a campaign benefit is a contribution.

In fact, the Edwards case itself disproves Giuliani’s point. Via George Conway’s, Trevor Potter’s and Neal Katyal’s Friday op-ed:

Edwards repeatedly argued that the payments were not campaign contributions because they were not made exclusively to further his campaign. The judge rejected this argument as a matter of law, ruling that a payment to a candidate’s extramarital sexual partner is a campaign contribution if “one of” the reasons the payment is made is to influence the election.

As a legal matter, that aspect of the Edwards case is what matters now — and it’s damning for Trump. It provides a precedent that other courts could follow in any prosecution arising out of the hush-money schemes Trump paid: The president could face criminal charges for conspiring with Cohen to make the payments because the evidence shows the payments were made, at least in part, for campaign purposes.

The second point is that Giuliani is moving the goal posts. The Trump team’s denials on this have been steadily watered down over time. Eventually, Giuliani and Co. admitted to the payments but said they were personal — the kind of thing Trump would have done even if it weren’t the eve of the 2016 election.

“I also think, personally, neither one of them saw it as a campaign thing; they thought of it as a personal thing,” he told The Washington Post in May. He told “Fox and Friends” the same day: “This was for personal reasons. This was — the president had been hurt personally . . . so much and the first lady, by some of the false allegations . . . It was to save their marriage — not their marriage, so much, but their reputation.”

But Giuliani doesn’t even seem to be holding that line any more. Implicit in his comments at the top is the idea that this wasn’t solely personal but, instead, served a dual purpose that included the campaign. “It’s not a contribution if it’s intended for a purpose in addition to the campaign purpose,” he said.

“In addition to the campaign purpose” means there was a campaign purpose. And when you look at actual federal election law, it suggests that Giuliani just conceded that this was a campaign finance violation that Trump has been implicated in.