It is perfectly safe to view the eclipse with the naked eye during the short period known as
totality. Most places don't experience totality though, so you have to make it out to a place that lies in the path of totality (which is relatively a pretty narrow band). I've heard this confirmed by several Astronomy professors and astronomy journalists. It's also explained on the Nasa website:
https://science.nasa.gov/eclipses/safety/
"
You can view the eclipse directly without proper eye protection only when the Moon completely obscures the Sun’s bright face – during the brief and spectacular period known as totality. (You’ll know it’s safe when you can no longer see any part of the Sun through eclipse glasses or a solar viewer.)"