A buddy mistakenly thought flutes weren't woodwinds, I think in part he was conflating "the reeds" with "the woodwinds" - easy enough mistake if you didn't grow up in symphonic groups.
Yamaha implies a definition of "woodwinds" as "the non-'lip reed' wind instruments" - i.e. you don't buzz your lips to make a sound.
The term "lip reed" seems a bit ridiculous, tho.