Interesting, my contact at Apple told me otherwise.
I am still highly skeptical, though. 250 passengers over 5 access points all watching video at the same time no problem? I doubt it.
More likely is that they use 64 GB iPads which do a lot of caching. Probably even some pre-caching before they put them in the aircraft. 80% of people will probably all watch the same 20% of total content, so that would work really well, while giving the impression of true streaming and from a user's point of view it makes no difference; they just want to watch movies!
Gotta love marketing!