Washington CNN  — 

President Donald Trump uttered fewer false claims than usual at the White House coronavirus briefing on Tuesday.

But he did make at least a couple. And he made other statements that were missing key context.

Here are some fact checks:

Harvard’s relief money

Trump threatened Harvard University, saying the institution took coronavirus funding “meant for workers.”

Trump was responding to a question about how the federal government would retrieve funds from large companies securing loans through the Paycheck Protection Program, which were supposed to be for small businesses. “Harvard’s going to pay back the money. They shouldn’t be taking it. … I’m not going to mention any other names, but when I saw Harvard, they have one of the largest endowments anywhere in the country, maybe in the world, I guess. And they’re going to pay back that money.”

Facts First: Trump misleadingly suggested that Harvard got money meant for businesses. Harvard did receive funding from the coronavirus relief money, but Trump didn’t distinguish between two separate sources of federal funding within the CARES Act coronavirus package – the Higher Education Emergency Relief Fund and the Paycheck Protection Program. The relief fund is primarily meant to provide financial relief grants to students. The paycheck program is a set of loans meant for small businesses, which Harvard never applied for or received.

Harvard, which has a roughly $40 billion-dollar endowment, received nearly $9 million from the CARES Act coronavirus relief package through the Higher Education Emergency Relief Fund.

The fund is disbursed through the Department of Education and was granted to a long list of colleges and universities around the country. It was established “to provide emergency financial aid grants to students for expenses related to the disruption of campus operations due to coronavirus,” according to the Department of Education. The DOE also points out that a formula prescribed by the CARES Act legislation predetermines how much money each college or university is supposed to be granted.

The Paycheck Protection Program, administered through the Small Business Administration, provides loans to small businesses to deal with the economic impact of the coronavirus.

The PPP also received funding through the CARES Act, but money for that program has been tapped out. Additional funding for the PPP was approved by the Senate on Tuesday.

In a statement, Harvard University said the school “did not apply for, nor has it received any funds through the U.S. Small Business Administration’s Paycheck Protection Program for small businesses.”

The statement adds that Harvard has committed that 100% of the funds it received through the Higher Education Emergency Relief Fund “will be used to provide direct assistance to students facing urgent financial needs due to the Covid-19 pandemic.”

The university added that these funds “will be on top of the support the University has already provided to students – including assistance with travel, providing direct aid for living expenses to those with need, and supporting students’ transition to online education.”

Georgia, testing and salons

White House coronavirus response coordinator Dr. Deborah Birx was asked about Republican Georgia Gov. Brian Kemp’s decision to allow nail salons, hair salons and tattoo parlors in his state to reopen. The reporter noted that people have to be close together at such establishments.

After Birx responded, Trump said, “Are they doing testing before they go in? We have to find that out. That’s why – I’m speaking to the governor in a little while, and I’ll be asking him those questions.”

Facts First: Trump was asking a question, not making a false assertion, but there are no known plans for patrons of Georgia nail salons, hair salons or tattoo parlors to be somehow tested for the coronavirus before they enter. Kemp has said nothing about any such testing.

Kemp spoke at length during a Monday news conference about his efforts to expand testing in Georgia, including through National Guard “strike teams” in virus hot spots and the use of university laboratories to process samples. But he did not say there were any testing requirements for people to enter the businesses that he said he would allow to reopen, nor any plans to offer testing in the vicinity of all of these businesses.

Social distancing protesters

The President repeated his assertion that protesters of stay-at-home orders in some states were following social distancing guidelines.

“And I’ve watched some of the protests – not in great detail, but I see that. And they’re separated…a lot of space in between,” Trump said. “I mean, they’re watching, believe it or not, social – they’re doing social distancing, if you can believe it. And they are. And they’re protesting, but they – the groups I’ve seen have been very much spread out. So, I think that’s good.”

Facts first: Protesters gathered in several state capitals to voice their opposition to stay-at-home orders issued by governors to slow the spread of the novel coronavirus. Some of the protests have involved participants keeping their distance from each other, but others have involved participants crowding close together. Trump didn’t identify which protests he has seen.

In Pennsylvania, hundreds of protestors gathered on the steps of the Capitol in Harrisburg as police barricades blocked people from advancing to entrances.

In Michigan, protesters drove cars to crowd streets around the state Capitol in protest, but some got out of their cars and crowded the steps of the Capitol building.

One attendee even told CNN affiliate WILX, “I think every single person here is probably going to get coronavirus, we’re all within six feet of each other.”

In Kentucky, protesters standing within feet of each other chanted “Open Up Kentucky!” and “You’re not a king, we won’t kiss your ring” outside the room where Gov. Andy Beshear was giving his daily coronavirus update on April 15.

Meanwhile, a striking image by Columbus Post-Dispatch’s Joshua Bickel of a protest in Ohio showed a crowd of protesters packed against doors outside the Statehouse Atrium in Columbus on April 13.

While some protesters did make the effort to follow social distancing guidelines during the demonstrations, any breaches of social distancing practices threatens to increase the spread of the virus.

Mexican soldiers and the border

Speaking about what he said were his achievements on immigration policy, Trump claimed that “Mexico has 27,000 soldiers right now on our southern border that we share with them.”

Facts First: Mexico has deployed around 27,000 troops, but Trump exaggerated how many are being stationed near the US border in particular; Mexico’s defense minister said in October that it was about 15,000 on the US border, about 12,000 on Mexico’s own southern border.

The trade deficit with China

Trump repeated his frequent claim that the US trade deficit with China used to be as high as $500 billion: “I even asked the leaders of China, how – how did this ever happen? Where our country loses tens of billions of dollars a year. And I don’t mean just tens. Take a look: $200 billion, $300 billion, $400 billion, $500 billion a year. How did they ever let a thing like this happen?”

Facts First: There has never been a $500 billion trade deficit with China. (Trump describes trade deficits as “losing,” though many economists dispute that characterization.) The 2018 deficit was $381 billion when counting goods and services, $420 billion when counting goods alone.

This story has been updated with more context for the Harvard example.