I have tried both strict Paleo and the keto diet, and not found this to be true in practice
Fun fact: one of the strongest withdrawals I have experienced was sugary drinks. To make matter worse it was just the middle of summer and drink of cold coke seemed to be a blessing. So I went to the store, bought a 6-pack of sugar-free semi-keto-friendly Coke, put it in the fridge and never took it back. Just the fact that I could get it whenever I want seemed to help :)