The problem was the same as stated in this question: AIR: securityError on OSX (but not on Windows) with URLStream() For some reason AIR in OSX is not using the security sandbox and the source file path for the video must be provided as an URL.
So the code should be like:
<s:VideoDisplay width="100%" height="100%" source="{new File('/somepath/video.mp4').url}"
mediaPlayerStateChange="mediaPlayerStateChangeHandler(event)"/>
That way it works in osx and windows.