Actually, you are Correct.
Dreamcast - November 27, 1998 <Japan>
XBOX - November 15, 2001 <USA>
Even if we go by the U.S. Release of the DC, it came out on 9/9/99 So yes, Sega did do it First
The reason i think people Call it the Xbox Layout, the Dreamcast's Controller, is kinda Forgotten by 90% of people. and or Misremember the OG Xbox as coming out before the DC. People here, for the most part Don't, but i actully had to look up when the OG Xbox came out <knew the DC did but couldn't Recall what year the OGXB came out>
And the XBOX is more ingrained in Gaming history Memory than the DC has been for Along time now, due to it's short Lifespan. Sad but True.