What D! wrote was, "a US 'visa waiver' does not cost nothing." So according to your belief Silver Fox, what he meant was "Does not cost anything", as in it is free. Really? I don't think so, he meant to say that they are NOT free. What you have done is correct the double negative to the single negative which is the usual correction. However, in this case the writer didn't actually mean to state a negative, he meant to state a positive. It costs something. It is possible to sometimes interpret a double negative as stating a positive such as in 'I don't know nothing' can be corrected to mean, 'I do know something.' That was the case here.

As for double negatives being common in the speech of some people, I agree, they are. Nevertheless they are not considered acceptable in standard English. Here is a good description by the Oxford Dictionary. https://en.oxforddictionaries.com/gr...uble-negatives

One of the reasons to avoid them is because they can be misinterpreted as you apparently did. What is a commonly accepted term in a local dialect is not something that should be written in a forum where your readers are not likely to be all from your own little region where such terms are understood. Communication is about being understood by the reader(listener), not by you alone.