OK I found the answer for JWPlayer:
From here
Add "controlbar.idlehide": true as flashvar
var player = jwplayer("ANIM_INTRO1").setup( { flashplayer: "/content/jw5.4/player.swf")", file: "test/FULL-VIDEO.f4v", streamer: 'rtmp://flvstream.example.com/cfx/st', autostart: true, height: 242, width: 555, "controlbar.idlehide": true, }
This seems like a pretty recent addition, as I also found some early posts (in the same thread) complaining that this was not possible - with code to fix the source.
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