Zenith-Add horsepower, NASA-add drag: to create lift. How is this possible?
Equating rate of climb with more lift is wrong. In order to climb the aircraft needs more thrust but a bit less lift. Therefore, the first statement is wrong: Adding more power does not create more lift. The only case where this happens is at high speed and the maximum sustainable lift coefficient: More power allows to fly at a higher load factor, but depending on the flight envelope, might result in a crash. The explanation does not make that connection, so it is wrong.

The second explanation is special for the X-57 because the concept uses the propeller slipstream to create blown lift. At low speed, the thrust needed to maintain flight speed is low and might not be sufficient to create enough lift on the small wing. Adding some drag allows to fly at higher thrust without climbing away. But only in this special case when most of the wing is in the propeller slipstream. So the second statement is correct but only for a single case.



Artist concept of the NASA X-57 Maxwell (image source).