Do you really think you can't download music over a dialup connection?
I saw nowhere in the article where it said she had a dedicated connection.
If you read the whole article, you will see that the daughter had songs on her computer available to others to upload from her computer. You can't really do that with a dialup connection. First, the upload bandwidth is too small, and second, other people would have to be online at exactly the same time you are on in order to upload your songs, and would have to be finished before you logged off. So the assumtion here is that she had a dedicated internet connection.
That being said, a DSL connection is not that much more expensive (about $25/month) than a dial-up connection ($10-15/month).