I'm going to state what I think the root of the problem is first and then explain a little more.
If I create a post as an administrator, I can include an embedded video (like from YouTube) in my post. If I create a post as a subscriber (I'll explain in a minute), I can stick the embedded video in the post and preview it, but when I click the submit button, it disappears and doesn't end up in the post.
Now, to me, it's obvious that somewhere in the WordPress Codex is some code that prohibits users of below some level (maybe administrator) from including an embedded video in their post. (The only other option I can see is that the permissions difficulty is on the TinyMCE side --more on that in a minute).
Does anyone know where this code resides so that I can hack it? I want subscribers to be able to include embedded videos in their posts.
Now, I'll explain why I want this seemingly ridiculous function.
I'm using a plugin, TDO Mini Forms, which allows users to submit a post even if they are a subscriber while not leaving the website (they do not go to the admin part of WordPress, which would scare off my users). I've also installed the WYSIWYG editor TinyMCE with advanced buttons, which include the "embed video" and "preview" functions, both of which work like a charm.