I spent a whole night battling to get secure http working in 'Movgrab', only to discover that no-one uses it. I couldn't find a single proxyserver that supported 'straight' https (some of them might support use of the 'upgrade' header, but as of right now, I don't understand that). So then I switched to using https to connect directly to video-sharing websites. Any google website (youtube, videos.google.com) bounces me straight to www.google.com if I try to use https. Many other sites let you use it for the initial connection, but insist on redirecting you to http: when you try to get video. The rest don't support https at all.
I don't know, I would have thought that in these days of 'Web 2.0' secure browsing would have been the norm by now.