President Trump invited the media into the Oval Office on Tuesday to hear part of his conversation with Senate Minority Leader Charles E. Schumer (D-N.Y.) and House Minority Leader (for now) Nancy Pelosi (D-Calif.). In short order, things got staticky.

At issue was a looming government budget deadline put at risk by Trump’s insistence that any funding deal include money for the construction of a wall on the border with Mexico. Trump said he figured $5 billion would be a good start, making no mention of his frequent campaign-trail assertions that the cost of building a wall would be borne by Mexico.

The exchange was fascinating in part because it directly contradicted the president’s tweets from a few hours earlier. Then, for example, he claimed that Schumer and Pelosi didn’t want border security; in the Oval Office, he went to great pains to say that they all agreed on the need for border security.

The contentiousness stemmed from Trump’s insistence that “border security” necessarily meant the inclusion of the wall.

"We need the wall. The wall is a part of border security,” Trump said at one point. “We need border security. The wall is a part of border security. You can't have very good border security without the wall, no."

“That’s just not true. That is a political promise,” Pelosi replied.

"The experts say you can do border security without a wall, which is wasteful and doesn't solve the problem,” Schumer added.

"It totally solves the problem, and it's very important,” Trump replied.

To make his case, Trump pointed to what he presented as the dangers of remaining without a wall.

“This is a national emergency,” he said. “Drugs are pouring into our country. People with tremendous medical difficulty and medical problems are pouring in, and in many cases it’s contagious. They’re pouring into our country. We have to have border security. We have to have a wall as part of border security.”

This, too, contradicts his tweets from earlier in the day: Then, he claimed that “Our Southern Border is now Secure and will remain that way.”

It's important to note that Trump's defenses of the need for the wall presented above are misleading, exaggerated or untrue.

Take, for example, his claim that “drugs are pouring into our country.” It’s certainly true that drugs are being imported into the United States. It’s just not true that the wall would prevent that from happening to any significant extent.

Illegal drugs “mostly come through the ports of entry” at the border, one senior administration official testified before Congress last year. In other words, most of the drugs that enter the country come through established border checkpoints, hidden in vehicles and then distributed throughout the country.

The official who made that point? Then-Homeland Security Secretary John F. Kelly. Another official testified in February 2017 that ports of entry “are the major points of entry for illegal drugs, where smugglers use a wide variety of tactics and techniques for concealing drugs."

One expert who spoke with The Washington Post about curtailing the influx of drugs figured that the cost of better securing ports of entry against drug smuggling would cost about — $5 billion.

Trump’s claim that immigrants bring infectious disease is a long-standing one. It arose in 2014, during a spike in migration from Central America, and he offered it during his campaign for the presidency.

PolitiFact looked at this in 2015, finding no evidence it was true. Last week, a new report documenting a two-year study by medical researchers looked at this specific claim. The determination? “There is no evidence to show that migrants are spreading disease,” one expert told NBC News.

"The two-year study found that international migrants are less likely than people in their host countries to die of heart disease, cancer, respiratory diseases and other ills,” NBC's report states. “The exceptions are hepatitis, tuberculosis and HIV. But the study also found these infections are generally only spread within the affected immigrant communities and not to the wider population."

Some of the reports of disease affecting migrant communities, the researchers found, were a result of the conditions of migration: exhaustion.

At another point in the conversation, Trump claimed that the government had also caught terrorists trying to cross the border.

"People are pouring into our country, including terrorists. We have terrorists. We caught 10 terrorists over the last very short period of time,” he said. “Ten. These are very serious people."

It’s not clear what Trump’s referring to. During the debate over the migrant caravan, Vice President Pence claimed that the government was apprehending 10 terrorists or suspected terrorists *a day* on the border, a claim that his office later walked back.

A report from the State Department last year undercut Trump’s point more broadly, noting that there was “no credible information that any member of a terrorist group has traveled through Mexico to gain access to the United States.”

All of this, mind you, comes before building any wall. Drugs flow in through the checkpoints that must necessarily exist on the border. Disease and terrorism aren’t seen as any significant threat. But Trump continues to insist on the wall.

Remarkably, Pelosi at one point tried to give Trump an out, suggesting that their debate occur in private, instead of in front of the cameras.

"Let us have a conversation where we don’t have to contradict in public the statistics that you put forth but instead can have a conversation about what will really work,” Pelosi said.

That conversation may have ensued. Trump’s questionable statistics were nonetheless offered.