read the crossfit nutrition prescription here:
Paleo diet is many things to many people. thepaleodiet is a trademark of Dr. loren cordain and he is strict about dairy (including oats), grains, legumes.
Other people follow a less strict paleo/primal nutrition plan with either some food group allowed or cheat meals inserted.
My suggestion would be to go on a 30 day strict Paleo challenge and after that slowly test what you can insert back into your routine without adverse affects.