True, it's a common misunderstanding. If it were true then headphones would only reach down to 400hz or so!
Wouldn't headphone cut off be more like 9000 Hz (13,500 inches per second, the speed of sound at normal atmospheric pressures/temperature, and assuming a 1.5 inch maximum dimension from headphone diagram to ear drum)?
By this concept earbuds would be even worse (virtually unworkable for human hearing).