What's the Deal, Arc System Works?

Arc System Works' history timeline, as seen in their 30th anniversary music video. On December 28, 1991, they "developed 'Sonic the Hedgehog'".

Why does Arc System Works take credit for Sonic 1 on Game Gear? That was developed by Yuzo Koshiro's company Ancient; they said so themselves. Yet Arc mentioned it in their 25th anniversary book and their 30th anniversary music video.

Maybe Arc converted it to the Master System? But the Arc book specifically lists the Game Gear version, and the music video gives the Japanese release date for the Game Gear version (see screenshot above). However, both Yuzo Koshiro (in The Untold History of Japanese Game Developers: Volume 1) and Ancient's Twitter account have said they developed the Game Gear version first. Hmmm...