According to technobabble, people don't age or grow up on Neverland because time doesn't pass there. This would logically mean that non-human life, plants included, shouldn't grow or age either. Now, we know that the inhabitants of Neverland still need to eat - hence the fishing nets, crocodile hunts, and webs spun by the giant spiders - but if nothing grows or ages, then all food sources would quickly become depleted and everything would starve. In fact, Neverland should be a barren waste because life could have never started there in the first place.
Maybe it only counts for people.
More likely it only counts for organisms not native to Neverland.
Oh, and the explanation makes no sense anyway. If there would really pass no time, for some strange astrophysical reasons, that wouldn't just result in nobody aging. It would result in absolutely nothing happening, since there is no time for it to happen.
I believe his Exact Words were "... time stands still for all those who come here."
How did Peter get back to England to meet the Wendy Darling?
Without access to the orbs, wouldn't he have needed go "the long way," through interstellar space?