Jetpack video embed fails on youtu.be URLs

If you have short codes from Jetpack enabled, video embedding requires the entire youtube URL, not the youtu.be shortened URL that you get when you click the “Share” button in YouTube.

Oddly enough, youtu.be URLs work on wordpress.com, which supposedly uses the same code as Jetpack, but exporting those to a 3.3 installation causes the loss of all embedded videos that use the youtu.be URLs.