Just because someone uploaded a video to YouTube does not mean they are giving it away to anyone who wants to download and use it elsewhere. Some may care, and some may not. Google, by default, protects everyones copyrights; not just big media.
You probably have no malicious intent. You just want to view the video later, offline. However, Google doesn't know that. The safest course for them is to prevent copying. If a person wants to give their video to the world for free, and free of any license agreement, they have other outlets.
As far as what Google employees can do, this is true of any computer admin. There are usually policies against it, but in the end you either trust the people managing the servers, or you don't.
Just like your doctor or the other professionals in your life. You either trust them to keep your stuff private and secure, you don't care, or you find someone else.