But, anyway, it seems that as secretary of veterans affairs, Dr. Jackson would not be tending to Mr. Trump so much as to the right-wing billionaires Charles and David Koch and others who support privatization of veterans’ health care and other services.

The man Dr. Jackson would replace as head of this long-troubled department, David Shulkin, whom Mr. Trump fired on Wednesday, was the highest-ranking holdover from the Obama administration and among the few Trump cabinet members with demonstrated ability at their jobs.

Dr. Shulkin had strong bipartisan support in Congress — he was confirmed 100 to 0 by the Senate — and was backed by almost all veterans groups. He guided important legislation through Congress, a rare accomplishment for this White House. These laws led to an expansion of the G.I. Bill for post-9/11 veterans, an easier process to remove bad employees and quicker appeals on disability benefits.

The department’s inspector general found “serious derelictions,” though, in the way Dr. Shulkin spent his time and taxpayer money during a European trip, during which he had improperly accepted tickets to Wimbledon. That’s a serious problem. But it’s laughable to think that this would be a disqualification for a president for whom corruption is a continuing business model and who has watched some cabinet members treat self-dealing as a perk.

So we come back to the Koch brothers. After a year of amity between Dr. Shulkin and the president, there came word last month of behind-the-scenes intrigue inside and outside the department over replacing the secretary. Those supporting such a move had ties to the Kochs and a group they fund called Concerned Veterans of America.