Never heard of it. Spent two minutes looking for it on the desktop (right-click I assume), and on the web interface. No dice.

Right click on the files/folders you want to share read-only, go to the Dropbox sub-menu, and click "get shareable link". I use it all the time. I think it's exactly what you're describing?

I only see "Browse on Dropbox website..." and "Share this folder..." in the contextual menu.

I don't doubt you at all – I can see in their documentation that the feature exists. I just can't seem to make it happen.

Update: Looks like this only works for files that are already public, as far as I can tell. I managed to find "Copy public link..." if I right click in the Public folder.

Update 2: What a mess! Here's the doc that explains this buried feature: https://www.dropbox.com/help/167 I was able to switch to the "new sharing model", whatever that means. I still can't generate the link, though.