I don't see how Epson would ever know if you used non-Epson inks. I don't know about their service policy, but it's possible that that information is accurate.
Hmmmm....maybe it's no more mysterious than reading the small print. I'm just setting up a new Canon and, in the section where you can agree or not to send information to Canon, it has this line about what is sent: "Usage history
such as the type of ink installed, ink usage information, the number of sheets printed, scanning frequency, and maintenance information, etc."
Because the premise is product improvement, I'm guessing most people think "well, sure" and click without reading. I'm also guessing Epson has similar language. Ergo: the fellow I first mentioned who had his service stopped.