While I think Peta would actually try something like that, I don't think it will actually go that far. I do think exotics are in trouble though. Personally I keep several "exotics". Ferrets, birds, snakes, rodents, and eventually lizards.
I think primates are a little different. I think there needs to be species specific regulations regarding keeping primates as pets. I just saw on tv yesterday, this lady had a brown cappuchin (spelling is terrible) monkey. She got her at 3 weeks of age. She was still a baby! She got her because she could not have a child of her own and apparently her husband said that for him adoption was out of the question. So they stole this little baby monkey away from her mother and cared for her just because the woman thought she needed a 'baby' to care for. Well when the woman finally had a baby, she thought the monkey would be aggressive towards the baby. Also turns out the monkey had developed diabetes due to too much human food. So they turned the monkey over to this sanctuary who is now currently caring for her. That is why I think that keeping primates should be under strict regulation so that people like this do not have primates. Primates are not substitute children. They are monkeys, not humans. They have specific dietary, environmental, and social needs.
If I ever decide I want to keep primates I am going to study my butt off and I hope there are regulations in place so that when I go to get a permit, I have to show I can truely take care of that monkey.
Many animals do not require permits though. I don't think non-exotics should have permits. Large snakes, venemous snakes, large birds, birds of prey, primates, and large lizards should all have permits.