Not true. Knowing the APIs you most commonly use instead of having to keep flicking back to the reference makes you much more efficient.
Your professor DID memorize them, he was just smart about how he did it. Instead of memorizing upfront, he did it in bitesize pieces, and was productive along the way. That's what a good programmer does too.
Chess champions use this technique too. I remember seeing a TV documentary where they got a chess champion to look at a board layout for a few seconds and reproduce it in front of them. They could do this easily for a valid board layout. But when they got people with no knowledge of chess to design the board layout in an invalid manner the chess champion could not reconstruct the board as accurately or as quickly.
I guess a common programming equivalent would be a design pattern.
That said, we're saying the same thing -- rote memorization without applied knowledge isn't worth anything. Learning by doing is the way to go.