When animals come close to extinction, as in the case of the Cahow, there is always the possibility of cross species heterozygous offspring as was filmed by the CahowCam just before 2am local time.
Rabbits from the colony on nearby Hen Island must have swum over to Nonsuch Island at some point in the past, prior to the Cahow rediscovery in 1951. The gene for the ears seems to be recessive, only appearing every few generations (with the offspring named a "Cabit"), however all chicks in the colony still hatch with soft grey rabbit type fur instead of feathers, which they then molt prior to fledging.
As explained by Wikipedia:
In general usage, hybrid is synonymous with heterozygous: any offspring resulting from the breeding of two genetically distinct individuals.