Koch continued fuming about their feud for years, writing in one essay that became public only after his death in 2013 that it was "incomprehensible" to him that some voters regarded Trump "as a folk hero."
Yet they did then. And many more do now.
Trump's willingness to attack opponents, often with only the flimsiest of evidence and sometimes with none at all, has played a huge role in his rise. So has his skill at manipulating the media into spreading his often-false charges. The playbook he uses is one he began practicing as a New York developer and has honed for decades.
"He gets the scent of malfeasance off of him by placing the blame on others," said Sheinkopf. "Every step is laced with the most extraordinary chutzpah that manages to work out well for him." 
Indeed, for a considerable segment of the electorate, Trump's stature grew even as he stepped up his exaggerations, distortions and often outright lies. Trump's unflinching embrace of the fringe "birther" movement, which falsely accused President Barack Obama of being foreign born, was not a setback for him, but a political stepping stone. His attacks on Hillary Clinton in 2016, greatly exaggerated as they were, successfully deflected attention from his own scandals.
Now, impeachment proceedings are hanging over him, and Trump is again counterattacking with misinformation. The impeachment inquiry is focused on whether Trump pressured Ukraine's government to help him politically by investigating the business dealings of Hunter Biden, the son of the former vice president, who formerly served on the board of a gas company in that country.
Trump's response has been to amplify unfounded claims about the Biden family's dealings there and elsewhere, and to revive previously debunked claims about Clinton.
Fact checkers at CNN tallied 66 false claims by Trump last week alone. He recycled a groundless conspiracy theory that the email server Clinton once used as secretary of state was being hidden somewhere in Ukraine. He falsely said that Hunter Biden had gotten a "payoff" in China, "where they give the son a billion and a half dollars," and that he had a photo of Joe Biden playing golf with the "boss" of a Ukrainian gas company.
The photo showed Biden with his son and one of his son's longtime business partners, who was on the board of a gas company, but was not an executive, let alone the "boss." The claim about China appeared to refer to a private-equity firm, BHR Equity Investment Fund Management Co., based in Shanghai, which sought to raise 1.5 billion dollars several years ago to invest in companies. The younger Biden sits on the fund's board, but has never been paid for that work, his lawyer says.
In both cases, as with Clinton's emails in 2016 or municipal corruption in New York in the 1980s, Trump's approach is to take a nugget of fact, wildly embellish it, then repeat his claims again and again as they get amplified on social media. The target then has the choice of ignoring the smear and leaving it unanswered or engaging in a debate with Trump that often further spreads the false charges.
When fact checkers step in to set the record straight, as they did with the purported photograph, Trump makes himself out to be a victim of "fake news." It has become one of his most effective lines of attack, causing media scholars to question if the press grasps the extent to which it is being used.
"Fact checkers have become part of the problem," said Whitney Phillips, an assistant professor at Syracuse University who studies media and disinformation. "We tend to assume that sunlight disinfects. It is a credo that you take something's power away when you call attention to its falsehood. But that is not how information travels online and it is not how people are arriving at their decision-making now.
"Throwing facts on these conspiracy theories is just throwing kindling on the fire," Phillips said. "If the mainstream press is debunking something Trump says, for many of his supporters, that just shows Trump is correct."
The role the press plays in transmitting Trump's smears is a source of consternation in many newsrooms. MSNBC, for example, recently interrupted its broadcast of a Trump news conference to point out that several things he had said were not true. Headline writers frequently come under attack for carelessly repeating false claims even in stories that pick those claims apart.
The issue also looms large for Democrats, who continue to disagree among themselves about how - or even whether - to respond to Trump's charges.
Democratic strategist Paul Begala advises his party's candidates to spend less time rebutting absurd claims and more time calling out Trump on why he is making them.
"Don't say, 'I am not a horse thief!'," Begala wrote in an email. "Contextualize the attack, objectify it, then use it to counterattack: 'Why is Donald Trump smearing me? Because he has 50 horses in his paddock with stolen brands on them. He is trying to distract you from his long career of horse thievery.'"
"Don't repeat the charge. Just dismiss it, explain to folks why he's doing it."
Other battle-scarred Democrats have different ideas.
Brian Fallon, formerly Hillary Clinton's campaign press secretary, argues Democrats will have their best chance by using the current impeachment proceedings to take control of the narrative from Trump.
A relentless flow of incriminating evidence, compromising witnesses and refusals to testify, he argues, will overwhelm Trump's ability to focus public attention on the attacks he launches.
"You can't hope to try to slug it out with them," Fallon said. "You can't hope to out-logic them, even if you get fact checkers to write 16 pieces about what Trump is saying is not true. You need to overwhelm them by using every piece of leverage you can to lift up competing story lines."
Yet some are skeptical that any strategy will work to inoculate Trump targets who are longtime establishment figures. Trump feeds off the mistrust a significant swath of the electorate has toward anything politicians say or do. It is why Clinton was so vulnerable to him.
"Whatever Hillary Clinton did, she was the establishment," said Robert Reich, the Labor secretary under Bill Clinton. "There was no way she could present herself as the champion of the working-class in America. ... Biden also has to cope with this anti-establishment surge that grows louder and louder."
Sheinkopf was even more downbeat about Biden's fate.
"Find another candidate," he said he advises fellow Democrats.
"Biden's son, whether it is fair or not, becomes the exemplar for bad American behavior overseas," he said. "Trump will make him corrupt enough to allow Trump to be the savior of the republic and protector of the bald eagle. This is potentially fatal for Democrats."
Washington Democrats "want to believe the American public is playing by a rule book that hasn't been used in years," Sheinkopf said. "Do they believe for 20 seconds that people who voted for Donald Trump really care what happened in Ukraine? The only thing that matters is what social media picks up."
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