Personally, I don't consider eating Neolithic foods 'cheating'. I basically follow Panu.
I'm pretty sensitive to what I eat especially my digestion, but don't get health consequences when I consume small/moderate amounts of many 'off plan' foods, and I highly doubt I'm unhealthier from eating them. I can't have small amounts of wheat and feel fine, so I don't. White rice, I eat all the time - it's totally harmless starch for me. If I eat too much total starch, I'm not going to feel well cause my blood sugar will crash, so I don't.
Now, a 'cheat day' involving binging on everything you usually don't have - I'm sure you'd feel like crap, and it would be very bad for you. But a few beers and a bite to eat here and there are probably not going to hurt you at all. If I were you of course I'd eat rice products but avoid wheat more stringently, even if you don't get symptoms from consuming it. A lot of the most prominent Paleo/health bloggers would agree - wheat is the worst grain even if you don't have celiac or gluten sensitivity.