I think your last paragraph is severely erronious. The original writer has become confused between passenger pigeons, a North American species which have, indeed become extinct, and homing pigeons, which are alive and well and being raced all over the world.
An edit would be in order.
Re: the last paragraph
As the original writer of this entry, I'd like to note that I was not the person who wrote that last section; it was later added by another user, which is clear if you look at the history page. Thanks. -K.C.