I think it would be more accurate to say that you can't do it without an external site
hosting your picture. You can then click on the little button shown in the screenshot below, and post the direct link within the tags that appear.
[ img ]
http://i.imgur.com/csVmmoR.png [ /img ] <-- Like so, except I added spaces around the "img" tags to demonstrate. It then shows up like below.
It's not super clear form your post if you are aware of this already, although it seems like you might be? I don't know. Imgur is a pretty good site for free image hosting. Imageshack used to be, but it looks like you have to pay now? I tried to post this image with Google Drive first, but that didn't work. It's really not hard to use imgur - uploading is easy, and they give you a direct link right there.