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).
Not to beat this into the ground, but I only have a dial connection and have downloaded & uploaded music at the same time. Sure its slow, but Im in no hurry.
I uploaded stuff on Kazaa a couple of years ago on dialup. It can be done but, as with anything dialup compared to broadband, it's a horrible option.
And you are right, at $27.95 my dsl connection is not really any more expensive than when I had AT&T dialup ($19.95).
High Speed Internet ($27.95)+ Online Game ($9.95)= cheap long term entertainment ($37.90 or @$1.25 a day). Cheaper than cable or a nice dinner and show.
I don't know about the others, but I know that Kazaa is quite advanced in that it can download the same file from multiple users at the same time (if there are other users who have the same file that you do, which is likely to be the case for anything you download from Kazaa).
So it is indeed quite possible to share files on a dialup connection, and if someone is downloading on a dialup connection, Kazaa will probably upload the files from users who are on dialup connections (those who are on DSL or cable connections are likely not going to be patient enough for that!).