Sorry, I could have been clearer.
I can ask about leprosy, in that I am curious about what this disease is, how common it is, etc, but I wouldn't ask for leprosy, because that means I want to have the disease.
So we know that "bede om noget" = "ask for something", but I would like to know the left hand side of the equality ? = "ask about something".
The difference is between "she asked" and "she did not ask". I am aware that they are regarded as synonymous, but logically, to ask for something (even nothing) is an active action, but to not ask for anything is passive. It's almost in the same category as the English, "I aint got nothing".