His response? "Well, PETA's never denied it!"
Well your friend is being dumb and arguing in bad faith. A quick web search will bring up their article about their stance on pet ownership. They encourage people who have the money, resources and time to care for pets to adopt and rescue pets.
Link: https://www.peta.org/about-peta/why-peta/pets/
and the very first sentence:
At PETA, we love and respect the animal companions who share our homes. Contrary to myth, PETA does not want to confiscate beloved, well-cared-for companions and “set them free.”
Anyone can say they are from some org or entity, but it doesn't make it true. Now if you will excuse me I am late for my space meeting at NASA today.