Pegasus, I think you're right. As far as EA's concerned, this is a matter of contract and not necessarily of copyright. But EULA's (i.e., terms of use contracts) are very hard to enforce and don't tend to stand up in court (if they ever get that far).
babyblue, I think your teacher may have been talking about trademarks, not copyrights. If they're not enforced, they break down (like Kleenex--the company tries very hard legally to prevent the use of the term Kleenex to refer to other facial tissues, because it will lose its trademark if the name becomes commonly used that way. Other examples are Scotch tape and Xerox.)