It’s now established that a secretive political group linked to the billionaire conservative activists Charles and David Koch has agreed to pay a record fine for violating California’s laws requiring the disclosure of campaign donations. But much else about these dark-money maneuvers remains shrouded in the mystery that inspired the title “Covert Operations” for the story I wrote about the Koch brothers in 2010.

How are the Kochs connected to the Center to Protect Patient Rights, which admitted to violating California’s campaign-disclosure requirements? The group is based at a post-office box in Arizona—a state where neither Koch brother has his principal residence. According to its most recent tax filing, its president is the Phoenix-based Republican political consultant named Sean Noble. The name of the organization makes it sound as if it champions patients’ rights—again, not a cause with which the conservative, libertarian, industrialist brothers have been especially identified. California’s attorney general and its Fair Political Practices Commission, which oversees the state’s campaign-finance laws, have fined the organization for failing to reveal that it was the true source of a stunning fifteen million dollars in 2012 contributions—aimed not at health-care matters but at scuttling a state initiative that would have raised taxes on high-income residents (while also modestly boosting the sales tax) and at promoting another initiative that would have curbed the political clout of unions in the state. (The donors’ side lost on both measures, in part because the huge amounts of last-minute secret money became a toxic political liability.)

California hasn’t been shy about mentioning the Koch connection. The Fair Political Practices Commission, chaired by Ann Ravel, described the Center to Protect Patient Rights as “part of the ‘Koch Brothers’ Network’ of dark money political non-profit corporations.”

And yet, yesterday, Melissa Cohlmia, a spokeswoman for Koch Industries, insisted that the brothers were not involved in the California campaign scandal in any way. Asked about Ravel’s statement, Cohlmia said, “Ms. Ravel’s comments were without any factual basis.” She also noted that a redacted list of donors to the California effort, which has surfaced in connection with the investigation, has revealed no contributions from either of the Koch brothers. “You will note there is no mention of Koch among the donors .… We were not involved in any of the activities at issue in California,” she said.

However, other documents that emerged yesterday in connection with the investigation suggest that many of those directly involved in the shady dealings believed that the Kochs were, too. Tony Russo, a longtime California political consultant who helped to raise funds to promote the union-curbing bill, and who later became a coöperating witness, told the state’s attorneys, “We thought we were dealing with the Koch network,” according to the Sacramento Bee columnist Dan Morain.

Russo told the attorneys that a donor to the Kochs’ organizations introduced him to Noble, who was identified as the Kochs’ “outside consultant.” Noble “thought the Koch network would be interested in helping fund a campaign similar to the one in Wisconsin, where Gov. Scott Walker attacked public-employee unions and withstood a recall,” Morain wrote, summarizing from Russo’s testimony.

The Fair Political Practices Commission also released an e-mail to Charles Koch, dated October 11, 2012, from someone whose name was redacted, in which the sender wrote, of the union-curbing bill, “It would be great if you could support the final effort with several million.” This person appeared to be on friendly enough terms with the magnate to chat breezily about getting together soon: “I look forward to seeing you on a golf course—probably after the election.” The sender also wrote, “I must tell you that Sean Noble from your group has been immensely helpful in our efforts.”

Is Sean Noble part of what the sender called the Kochs’ “group”? Is the Center to Protect Patient Rights part of their political apparatus? Numerous news accounts have described Noble as having represented the Kochs’ political interests at meetings with Karl Rove’s group American Crossroads. Noble has also been widely reported to have attended and spoken at some of the semi-annual political seminars that the Kochs host for high-dollar donors. Recently, Peter H. Stone, of the Huffington Post, quoted a G.O.P. operative who described Noble as “the wizard behind the screen” of the Koch brothers’ network.

Meanwhile, as recounted in Politico, records show that in 2012, a new, Koch-tied political nonprofit called “Freedom Partners” was by far the single largest source of cash to the controversial Center to Protect Patient Rights. And Stone reported that in 2011, according to I.R.S. records, “the largest chunk of the center’s funding to date has come from one group, Freedom Partners … which contributed a hundred and fifteen million dollars to the organization.”

So what, precisely, is the relationship between the Kochs, Noble, and the Center to Protect Patient Rights? Noble didn’t return numerous e-mails and phone calls asking about this. An attorney representing the Center to Protect Patient Rights issued a press release emphasizing that the group acted “in good faith” with “no intent to violate campaign reporting rules,” but leaving any connection to the Kochs unexplained. And when pressed on this, Cohlmia, after answering several other e-mailed questions, simply ceased to respond.

According to California’s attorney general, Kamala D. Harris, finding out any more will require a change in campaign-finance laws. In a statement, Harris said, “This case demonstrates in clear terms that California’s campaign-finance laws are in desperate need of reform. California law currently contains a loophole for certain groups to evade transparency by maintaining the anonymity of their donors.”

Above: A rally in Beverly Hills. Photograph by Joe Klamar/AFP/Getty.