erm. NO I read newspapers where poeple that have been in jail for years and never been to school now earn good in web hosting. Similer issues with other related businesses too.
It can't hurt! Online business mainly fail in the early stages because people aren't prepared for the time, hassle, cost, and most importantly, the lack of business knowledge. Can it be done? Hell yea! Can it be very beneficial to have a degree? Yes!
You do have to have ambition and a good dose of common sense, though. As to the "why or why not" part of your post, I would say that there are few courses available to get a degree that fully covers the way business works on the internet. You can learn marketing from reading, studying and trying what you've learned. When teenagers can run successful online businesses (and more of them do this every day), then obviously a degree isn't necessary. A degree isn't needed to run a successful business offline so why would it be needed online?
You "don't" need one, however some things you learn in school are valuable. In my own experiences, school sharpens your already existing natural qualities. For example, it makes your logical though process think critically. With that said, a good portion of online entrepreneurs ARE online entrepreneurs because the current model of education/school doesn't suit them. I believe it's an asset, but not a mandatory one.