No, I think you are correct. I spoke to a native speaker at work. He said "al mattino" would mean in the morning. The distinction is that mattino/a (not sure why there are two) is more specific - it is distinguishing the morning vs. say the afternoon.
My confusion was that sometimes giorno is used to mean "morning". But that is more of an idiomatic thing, e.g. buongiorno (which is really good day, technically, but said in the morning).