Brakes WordPress Twitter oEmbed support

WordPress has it’s own method of embedding tweets, but for a strange reason, I couldn’t make it work on my blog.

Then I’ve decided to start disabling one-by-one my plugins until I find the “culprit”.
When I’ve disabled Embed.ly, finally tweets begun embedding just fine.

Unfortunately I found no easy way to disable Twitter support (no such button on the settings page) so this is a deal-breaking for me.