When invited to a party, I will always ask this. If the answer is "Nothing, we've got it covered," or some variation of such, I take that to mean that I do not need to contribute to the refreshments at the party. Depending on the type of party we will sometimes bring some wine, but I don't expect it to be served, it's more of a hostess gift.
My husband and I host an annual part which is a backyard BBQ/pool party that involves high-school aged kids and the parents/family of those kids. It's casual, burgers and dogs, chips, soda. We don't serve booze for the adults. Every year, the parents ask what they can bring. Every year, I reply along the lines of, "Thanks so much but we've got everything we need, unless someone has dietary restrictions... etc..." most people take this at face value, but I have a few tenacious peeps who just will not take no for an answer!
"But you are feeding all of us! I have to bring something!"
"But I refuse to show up empty-handed!"
"Please let me bring something."
None of these people are being intentionally rude, I'm sure, and I feel all have their hearts in the right place. I have taken to asking people to bring extra beach towels because it can get kind of chaotic around the pool area. Am I being the rude one here in refusing help? Admittedly I can be a bit of a control freak so maybe I just need to let it go and start telling them what to bring, but just the thought of that sort of chaos in terms of food mish-mash makes my skin crawl.