If the company says peanut-free and contains tree nuts, I would guess their tree nuts weren't cross contaminated. Blue Diamond is one I know of that says peanut-free and has a good reputation as such. I heard there is a pistachio company out there too that is peanut-free.
My mum (peanut allergy) eats nuts and various cereals that contain nuts and are labelled peanut-free.
Chapman ice creams are peanut and nut free. I would be very careful with other brands, as I have seen many label for free from certain allergens only to see they are still made on shared lines with those allergens. Coconut dream is misleading that way - I don't trust their labels though many others here do. I guess it comes down to personal comfort zones. When in doubt, call the manufacturer and ask for all the allergen details.