I was able to get a working embed as follows:
Any try to get “https://www.youtube.com/watch?v=RtKF4H20NeA&feature=related” in the post by itself or to go inside an embed tag did not work per my post above.
I went to the Youtube website, and got an actual embed URL from the video. Once I pasted “<iframe width=”640″ height=”390″ src=”//www.youtube.com/embed/7A5Zi4veaw8″ frameborder=”0″ allowfullscreen></iframe>” into the post, it shows normally.
This is a vanilla install with no plugins active. It’s a course in WordPress, so it’s very basic.
Maybe someone with deeper knowledge can explain to the rest of us why the first URL would not result in a working video, and why the embed tags kept “spitting out” the first URL.