I'm using 1.9.11 but I believe everything I describe is in the same general areas.
There are a couple things you will want to check if you are trying to embed videos using the Embed code.
- Check the role permissions to see if that role has ALLOW set for the permission TRUST SUBMITTED CONTENT. Further discussion on topic.
- In Site Admin > Security > Site Policies, check to see what you have for the Allow EMBED and OBJECT tags and Enabled Trusted Content settings. Read the descriptions and switch to enabled if you are sure you want to do so. Further discussion on topic.
That should get you all set if you are trying to use the embed codes. The way I read the settings (someone correct me if I am wrong) is that forums work differently than other places that you will see the HTML editor. For example, a label can be created by teacher or higher role by default. So in essence, they have control of the course so they are to be trusted. The forums though have other people posting with lower permissions who may post objectable videos. So with the above settings set to No, it is stripping out the code which may contain objectable content for your own safety.
A better option in my opinion is using the YouTube filter (Site Admin > Modules > Filters > Multimedia Plugins). If you have that the YouTube filter enabled, you don't have to change the above settings. To embed a video, you simply enter the URL of the video.