Agreed, that's wrong.
Jang Doo Jin's Baduk Clinic was made by GoldenBell and it's their only (Famicom) title (they apparently planned a RPG as well but it never came out, it seems the company was short lived).
Kuk Je licensed pretty much all the somehow educational sachen games and some eventually had different startup logos but overall they are mostly the same to their sachen counterparts. I think they released like 3 or 4 at most?
I just know that K-002 is Magic Mathematics. Olympic IQ is K-003. Magic Cube should be K-001 then. Or K-004?
Also not all of them have a Kuk Je starting screen. Magic Mathematics is the same as the Sachen release I heard. While, according to these auctions, Olympic IQ may be completly different. And according to TCRF, Magic Cube also has a Kuk Je starting logo hidden in the game code (which should be activated in that release, assuming).