It is more likely that Safari is blocking the Flash plugin used by Youtube. This sometimes happens on videos uploaded prior to the switch to HTML5, or if the Flash variant of the Youtube embed is used.
Can you share your document?
One way to force HTML5 (which does not use plugins) is to add a query string at the end of your embed code.
Here’s an example:
<iframe width="420" height="315" src="https://www.youtube.com/embed/Qfo_2toNaGI?html5-1" frameborder="0" allowfullscreen></iframe>
The html5-1 query string property will encourage the player to load a plugin-free player.