Sounds weird, because we're used to media spam. But "drone" wrt. flying machines basically has 3 popular meanings - RC multicopters, any RC aircraft, and those big RC aircrafts with surveillance cameras and Hellfire missiles. Back because multicopter mania caused all RC aircraft to be rebranded as "drones", we used to call them by category - RC plane, RC helicopter, etc. So personally, I'm totally fine with NASA using the word "helicopter" - though I expect the name that's even more cool than "drone" - an UAV.
When i think "quadcopter", I think of something smaller than what NASA has proposed.