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.
Simply running alternate servers, distributing patches to the game, and using their launcher without copyrighted artwork or branding (maybe a "not endorsed by or associated with EA" sort of disclaimer) would seem to be fine.
It's reminiscent of the EverQuest server emulation community. They distribute patches and run open-source server infrastructure, but forbid distributing copies of the EQ game itself, pointing people to legitimate acquisition methods.
Then the legal system isn't trying to mandate specific implementation details.
But then people at least have a chance to know what they are buying.
I find this much less problematic than the idea that support will be eternal for a $50 game.
They weren't exactly "homemade" servers either. There was an entire industry of game server rentals and these were datacenter rack servers connected to fat pipes.
It wasn't unusual at all to find third-party servers with way better pings (and higher player caps) than the official servers.
I don't remember the official bf1942 servers ever having 32v32 player matches but that was fairly common for thirdparty servers for example.