hi
this is NOT a problem with people incorrectly using the wrong URL. I have the same problem. Check out this video of it:
https://www.dropbox.com/s/y042q9otmhv6jlh/wordpress%20wont%20embed.mp4?dl=0
If I Paste the link, I get the little image embedding icon but then it reverts to text.
If I use [embed] tags I see an error when I Save Draft and only a link when I publish. I have disabled all plugins and have tried this with TwentyFourteen active (not shown in the video)
