^well, technically it can be thought of as a cover because the original composer (Nosheen), who made the demo, made a music video for her version of the song. so some people argue that she "promoted it" so it's her song.
but in reality Nosheen's was just a demo and Kumi and avex have the rights to the song.
EDIT: here's her facebook page. you could listen to a remix of it.
http://www.facebook.com/pages/NOSHEEN/29753817816
she also commented about Kumi releasing the single. "Hey Guys. A little delayed but my song Physical Thing was released in Japan recently by an artist Kumi Koda! It went straight to No.1! No.1 hit songwriter baby! Check it OOUTT!"
so yeah, its Kumi's song.