Yes, you can, it just means that the issuing agency is no longer the embassy. So, because all renewals have to go through the US, it will take longer, but I don’t remember it being dramatic.
It looks to me like the passport itself is issued out of New Hampshire, but will still be distributed via the expatriate’s local embassy or consulate. It’d be ridiculous to demand that expatriates fly back to the US for this purpose: not even the US government is that stupid.
You’d be surprised. 
I stand corrected, though - I just skimmed over the piece.
Of course you can renew your passport outside the U.S.! just as I did last year. You download the forms, send it in by mail or courier service (I used FedEx) and the your passport comes in the mail. I didn’t have to set foot in the U.S. to do it.
However, what used to happen is that you could take your paperwork to the embassy and they would process it. Now it’s processed in the U.S. at a national center. I actually found it a little bit faster renewing my passport by mail this time than I did renewing it at the embassy the last time.
To be fair it was titled in a pretty obfuscatory way. Whoda thunk it?
Here’s an article about this exact subject and people giving up their US citizenship because of it.
http://www.time.com/time/world/article/0,8599,1983238,00.html?hpt=T2
Yes, my previous passport was processed by the embassy in Budapest, and it tended to get me extra scrutiny at borders. The photo was not laminated into the page–just kinda glued on top. The main security measure on the photo was two stamps: one ink, and one a raised seal. The photo was also on a page on its own, separate from the vital stats. It totally looked fake to me. On the plus side, it took about two or three days to get, and it contained 48 pages, so I didn’t need to add pages to it at any point.