Oh right, I think I miss understood. I was imagining you were getting data from them, not the other way around. Oops. That way would work.
Rather them using an iframe, then would so something like;
<div id="output-box">
<?php
echo file_get_contents("http://www.domainname.com/embedcontent/165/");
?>
</div>
That would then allow them to style the received data with CSS or something. With your idea or mine there are still big limitations. Since they will then have to trust your data. An iframe would enforce a bit more security but it wouldn't allow them to change the style on it (easily). However, I think you might want to control the formatting, so an iframe will do the job...
The best way by far would be a Soap or REST web service. However, that requires a bit more work than your proposed way.