I am Worried About something (Copy rights)

[Your Computer]

Except copyright laws really only apply when a profit is being made. If copyright issues really extended to custom-made, free content then sites like YouTube wouldn't exist. This is why agendas like SOPA have been shot down.

Typically, if say a mod of a game uses a song from so-and-so, as long as they are credited for their work then there is no issue. Again, usually only as long as no profit is being made.

You are forgetting the uploaders of the custom-made content are generally the authors of the assumed content. In which case it is obvious that they are permitting YouTube, and only Youtube (unless they specify a license other than the Youtube license), to host their content. This does not in anyway imply, except by explicit declaration of a differing license, that downloading the content with, for example, a browser plug-in and distributing the content thereafter is in anyway intended by the author of the content. In cases where the uploader is not the sole owner and author of the content and has no permission to distribute said content, YouTube reserves the right to take down the content (and lock or delete the YouTube account).

If you haven't noticed (though many people often don't care to read things like EULA), mods tools are released with the assumption that the user will develop content only for, and use content from the game which, the engine the mod tools were designed for and for personal, non-commercial use only. These things do not state that it is perfectly fine to include content which you have not created and have no rights to. After all, these things explicitly acknowledge local and international laws.