Anyway, I've tried adding &fs=0 before (although fs=0 actually removes the fullscreen button , fs=1 puts it back) and it makes the icon clickable, but nothing happens when you click on it.
As you can see it simply greys out and is unclickable after 1 click and no fullscreen ofc.
I'm not sure where you're getting the default youtube iframe stuff from, but according to the youtube player api (https://developers.google.com/youtube/player_parameters) that attribute is not used with an iframe, it was used with the old method of embedding a youtube video. Also checkout the link because the link that you've reported as being generated does not seem correct either. The link you posted in the op goes to www.youtube.com/v/ instead of www.youtube.com/embed/