When an organism is genetically modified, they have to test the animal to make sure that the gene "took." To do this they use a genetic marker for antibiotic resistance. If the organism is resistant to the antibiotic, they know that the gene transfer was a success.
So, when you ingest GMO food, you are ingesting antibiotic resistance. What happens if there is a mutation in the GMO organism? It could be a resistance to a new or important antibiotic.
This aspect of GM food is not at all regulated by the government (USA, not sure about the rest of the world), so every GM animal or plant has the potential to cause common yet serious infection to be untreatable. Then what happens when this gene escapes into the wild as they have done and are bound to do? The wild food supply carries this gene and increases the risk of mutation even more and the wild food supply may be lost to human consumption forever.
So the answer to your question is that any food that has the ability to create a super virulent disease that we can't even treat is as far from paleo as possible.
I didn't even address the concern about the "desired" genes and what problems those can cause when the escape into the wild.