Walensky’s comments came early this week in a conversation with Rachel Maddow on MSNBC, which Maddow introduced by saying that “Dr. Walensky is a scientist. She’s not prone to hyperbole. She sticks to the facts and the data.”

Critics argue Walensky didn’t live up to that introduction. They’ve honed in on statements made just moments into the interview:

“We can kind of almost see the end,” Walensky said. “We’re vaccinating so very fast, our data from the CDC today suggests, you know, that vaccinated people do not carry the virus, don’t get sick, and that it’s not just in the clinical trials but it’s also in real world data.”

The idea that vaccinated people “don’t get sick” is, on its face, an overstatement. “It’s much harder for vaccinated people to get infected, but don’t think for one second that they cannot get infected,” vaccine researcher Paul Duprex told the New York Times. The vaccines being administered in the U.S. are highly protective against COVID-19, but there is still a chance of infection.

A CDC spokesperson clarified in a statement to the Times that “Dr. Walensky spoke broadly during this interview … It’s possible that some people who are fully vaccinated could get COVID-19.”

But given that caveat, Walensky’s statement is largely accurate: vaccinated people are 100% protected from severe cases of COVID-19, and from the risk of death. This has been well-established for months.

Critics cited by the Times may also have overlooked the context for Walensky’s comments. As Maddow made crystal clear in her introduction to the segment, the most important finding of the recent CDC study was that vaccinated people suffer an extremely low rate of asymptomatic infections. This may be bigger news than the general public realizes.

“It means instead of the virus being able to hop from person to person to person to person, spreading and spreading, sickening some of them but not all of them, and the ones it does’t sicken don’t know they have it and they give it to more people,” Maddow explained, “Potentially mutating and becoming more virulent and drug resistant along the way, now we know that the vaccines work well enough that the virus stops with every vaccinated person.”

When Walensky said vaccinated people “don’t carry the virus,” she was likely referring, somewhat loosely, to this low incidence of asymptomatic infections. To translate it into the level of precision her critics would prefer, vaccinated people “have a very low chance of carrying the virus without showing symptoms of COVID-19.”

The big, major point, as Maddow put it, is simple: “We can end this thing.” Vaccinations not only prevent illness and death, they give the virus nowhere to hide. With enough vaccinations, we now know that COVID-19 can be truly controlled, even eradicated—like smallpox, yellow fever, and polio before it.

Critics like health policy expert Dr. Peter Bach argue that “This opens the door to the skeptics who think the government is sugarcoating the science,” as he told the Times. But it’s not clear that more cautious communication increases trust in health authorities, either. There’s evidence that the most accurate, detailed communication about risks can actually increase people’s doubts about the vaccine by giving the impression that the vaccine is less effective than it actually is.

That double-bind may not have an easy solution.

“Public health experts generally rely on scientific evidence to make recommendations to the public, and we have found ourselves in a challenging spot with the COVID-19 pandemic,” Dr. Janet Baseman, an epidemiologist with the University of Washington, told Fortune. “It is a new virus and so little evidence has been available to us at the time that we needed it for making timely recommendations.”

In other words, Walensky may have painted the good news with a slightly overbroad brush.

But make no mistake: The news is good. It is very, very good.

Now go get that shot.