There's a very wide interpretation of what it means to dress formal or even "resort casual"
If you go to a formal night dinner dressed in shorts and a t-shirt, you may feel very out of place, but I've not heard of people being turned away (though in my personal opinion, I wish they would direct people that are inappropriately attired to a more suitable dining option such as room service or something on deck 9).
Palo's isn't very strict either from what I saw though they might turn someone away in shorts and t-shirt.