This whole post may seem like I'm pointing out the obvious, but if there's one life lesson I've learned it's never assume people think the same way you do.
I think that a lot of people separate "reading" from "browsing the internet." Reading involves sitting in a cozy spot and getting lost in your own little world for a few hours. For many it's an intellectual pastime. In this mindset, reading things on the internet does not count as "reading."
Browsing the internet is its own activity. Unless you're trying to research something, internet browsing is usually not taken very seriously. You end up clicking on random links and before you know it you're up-to-date on Paris Hilton's latest breakup.
I would say that I definitely fall into both of those categories. But I would like to make people aware of a third option: you can "read" while "on the internet." Personally, I don't like staring at a computer screen for hours which is why I will step away when I want to read a novel. But short stories don't take that long to read. A five page short story will probably take you less time to read than watching the video on the tragic Paris Hilton breakup.
Even better is that there are thousands of free classic short stories online. You can find tons of public domain (author is dead essentially) works and not even have to leave your chair. So if you're in a situation where cozying up with a book isn't an option (say, on a break at work), short stories aren't a half bad way to go.
This isn't intended to be a sermon or anything. I just wanted to make people aware. It doesn't have to be mind-improving reading vs. brain-numbing internet.