McKinsey says the way the fund is structured and operated ensures that its employee investors do not stand to benefit from the firm’s inside knowledge and consulting advice. Hedge fund managers do not coordinate with McKinsey consultants, the firm says, and about 90 percent of MIO’s capital, including the Valeant investment, is managed by outside funds.

“MIO and McKinsey employ separate staffs. MIO staff have no nonpublic knowledge of McKinsey clients,” the company said in a statement. “For the vast majority of assets under management, decisions about specific investments are made by third-party managers.”

But those assurances of church-state separation are increasingly, and very publicly, being challenged, in Congress and in lawsuits alleging that McKinsey failed to fully disclose conflicts of interest in its work advising companies going through bankruptcy.

In one of them, a federal judge in Virginia last month reopened a coal-company bankruptcy case after learning that McKinsey had not disclosed, as required by law, that it was also among the company’s secured creditors, through MIO. The secured creditors recovered the most money. “These are some of the most serious allegations that I have ever seen,” said the judge, Kevin R. Huennekens.

Among the revelations in that lawsuit was that the head of McKinsey’s bankruptcy practice was also a member of the hedge fund’s board. Indeed, nine of the 11 people identified as MIO directors are current or former McKinsey consultants.

[McKinsey has agreed to pay $15 million to resolve a Justice Department investigation of its disclosures.]

In Puerto Rico, where McKinsey is advising a board that seeks to reduce the island’s crippling debt, The New York Times reported last year that the hedge fund was invested in bonds that gave it a stake in the outcome. Afterward, a bipartisan group of House members introduced a bill to compel advisers like McKinsey to disclose potential conflicts of interest. And Representative Nydia M. Velázquez, a New York Democrat, and Senator Elizabeth Warren, the Massachusetts Democrat now running for president, wrote to McKinsey, assailing its conflict-of-interest disclosure as “opaque or nonexistent.” McKinsey responded that there was no relationship between its work in Puerto Rico and the fund’s bond investments.