Skype 4 Business itself is just Lync rebranded, as it had nothing to do with Skype beyond a half-hearted bridge at one point. And you can still see references to lync in the domain names teams sets up.

I'm curious, why does it have to be a video? Is that a better proof in any way? Wouldn't you then say "oh we can't know if the video is actually authentic"?

Because it's easy to see and for people that don't have the software (like me) to see something approaching evidence.