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It is confirmed and the algorithm has been reverse engineered, though not by looking at firmware

https://w2.eff.org/Privacy/printers/docucolor/

Seems like the algorithm is simple enough that they did it just by looking at some prints

No need to reverse engineer, printers are required to do this for decades.

And the reason why it refuses to print this B&W document when yellow is empty.

You'd still need to reverse engineer it to build a better firmware without this anti-feature.

You don't need reverse engineering if it's publicly known fact for 20+ years, telemetry just identifies you. 20 years ago, you would need to find the printer.