The actual content of EA's letter makes it quite clear they are specifically after the unauthorized usage of their branding and trademark, and the fact that the site hosted the actual Battlefield Heroes game binaries for free download. The letter does not demand the site unilaterally shut down its server hosting. The site's response is arguably a big overreaction by the administrators, and most of the comments here seem to be misreading the events the same way.
There's a potential debate to whether EA should still "own" the right to block distribution of Heroes when there's no other way to acquire or play it, but debating whether or not EA has the right to shut down player-hosted servers is unrelated to the subject at hand. They do have an established right to enforce the use of their trademarks (logos, branding, etc) on a fan site like this.