Hi Haki Saki,
May I know which video specifically you are referring to?
I tried sharing the latest video uploaded(MMA Podcast) and I get this(http://take.ms/qC5NI).

Then I changed the privacy of the stream to 'Everyone'. Then I used Facebook's sharing debugger to crawl the stream item again. This is what Facebook managed to get from the stream item(http://take.ms/FGXD2).

Facebook is like a guest user when trying to get content from your site. So whatever content that is not available to guest users, will not be available to Facebook as well.