The article has tricky wording. Levi doesn't say the Palins are denying him visitation with his son. He says they're not allowing him to spend time alone with his son. IOW, he wants unsupervised visitation. Given his mother's drug bust, I can understand them denying him "alone" time.
In any case, if he and Bristol had married before she became pregnant or, at the very least, before the baby was born, he could be with his son everyday right now.
Innocent until proven guilty.