I looks like they're referencing this paper[1] which suggests that like dolphins, birds can sleep 1 brain hemisphere at a time. That's pretty interesting.
[1]http://www.nature.com/nature/journal/v397/n6718/full/397397a...
[1]http://www.nature.com/nature/journal/v397/n6718/full/397397a...
[1] https://en.wikipedia.org/wiki/Unihemispheric_slow-wave_sleep