Cubana is indeed allowed to fly throught the American Aerospace but with some restrictions. Not that I'm a real pilot, but I have both flown on ACA964 and CUB180, ACA reach Cuba faster than Cubana's flight, I therefore don't see any other eason other than restrictions to fly over certain airspaces.

ACA uses an A319 and Cubana a leased A320 from Grupo TACA