On a browser with flash the player loads in html5 mode with the following code. The sandbox prevents the iframe from accessing any plugins including flash.
<iframe sandbox="allow-same-origin allow-scripts allow-popups"
id="foo" width="100%" height="90%"
allowfullscreen="" webkitallowfullscreen="" mozallowfullscreen=""
src="http://player.vimeo.com/video/28544156?api=1">
</iframe>
To allow the vimeo button to open the vimeo web page for the video you need the 'allow-popups' permission. It's not needed to play the video.
Edit: adding complete example
If you had just a black view it's possible that the video had a size of zero because I had the iframe set to fill parent with width 100%, but if the parent was shrink to fit then that size would still be zero. Here is a whole web page with the CSS to make the video fill up most of the page. Additionally the -webkit-transform will mirror image the video, and then rotate it slightly. If it was displaying in flash this would produce a black screen as it can't handle rotations at all. I have since found out that this probably won't work on firefox at all because it doesn't natively support h.264 which is all vimeo serves, and disabling plugins will disable whatever plugin is making h.264 work on firefox.
<!DOCTYPE html>
<html>
<head>
<style>
div {
display: inline-block;
top: 0px;
left: 0px;
bottom: 0px;
right: 0px;
position: absolute;
}
iframe {
-webkit-transform: scaleX(-1) rotate(2deg);
}
</style>
</head>
<body>
<div>
<iframe sandbox="allow-same-origin allow-scripts allow-popups"
id="foo" width="100%" height="90%"
allowfullscreen="" webkitallowfullscreen="" mozallowfullscreen=""
src="http://player.vimeo.com/video/28544156?api=1">
</iframe>
</div>
</body>
</html>