I think this one of those situations where looking at an event through the lens of how people feel about a certain subject can change how that event is interpreted.
Fauci's statement was aired on 2020-03-08. I didn't dig into when it was recorded, but I'm assuming it takes a least a week to edit and air an episode. So very early days in the pandemic, and well before the hospitals were getting overwhelmed with patients (side note, I work in large-scale health care).
At about 10 seconds into this video excerpt of the interview, Fauci states, "The masks are important for someone who's infected to prevent them from infecting someone else."
From my point of view, that brings us to the biggest problem with understanding and reporting on the mask mandate. It was never about keeping the wearer from getting Covid-19, it was only ever about reducing the speed at which the virus spread, so that hospitals could keep up. That's it, and it does work. Even the crappy cloth ones help a little in that effort. Unless all standards are followed and using N95 type masks, they don't prevent anyone from getting a virus, but it will mean the rate at which a virus spreads across a population is slowed.
I can't tell you how many times I heard low-level, undereducated health care workers say in private something like "It should be MY choice!" What??? Your choice to infect other people? Your choice to cripple the US health care system and make your job vastly more difficult? Your choice to send the elderly to the ICU? No, they meant their choice as to whether or not they get infected. Dumb, but sure it's their choice. That's not what the mask mandate was about and the fact that they were saying that indicates they had no idea what the masks were really for.
In order to push their stock price through increased ad revenue, some news organizations chose to intentionally misreport mask use to make it seem like an attack on personal liberty when they should have framed it as a nation coming together to bolster the health and well-being of the citizenry. They did this even as their most vocal talking heads were fearful of contracting the virus and strictly adhering to the mask mandate.
But people want to belong to tribes, regardless of how harmful they are.