How many server owners/admins (current or past) have had any problems with Gravity or any other company, regarding your private server?
I assume u are not talking about the client side Gravity Error xD.
From all the things I heard from eAthena, Gravity did not send out any legal threat to private server directly. However, other local license holders such as LevelUpGames (Philiphine? Brazil?) and GameFliers (China/Taiwan?) were reported to have sent out DMCA to private servers with owner (or hosted?) from their licensed countries. I think at one point GameFliers went as far as getting the police involved and hunt down a home-hosted private server. The hoster was arrested right on the spot.
However, there could always be the case where private server send out fake DMCA to competitors to see who would chicken out and close their servers. So it's hard to say if any of them are real.
Might want to bring up stories of major servers got closed with rumor of "closed by gravity" hanging around it. Can't think of any at the moment.
They didn't sent directly to eAthena but instead to some of their developers like Ancyker and some others that ended in fails since eAthena is open source.
At France, fRO aka Gravity Europe closed every single pserver there too by sending e-mails to every server about going to court with them if not closed since RO was licensed by them there but ofc, some evaded that by hosting their servers outside of france and still rumble out there.