When Ryan introduced David he specifically said “here is David Cook singing Chris Cornell’s version of Billie Jean”, so for the second week in a row David DID NOT take credit for the arrangement he made sure the actual arranger was credited.
It was also a case where the Chris Cornell version differed so much from the original that it was almost unrecognizable as Jackson's song. This constitutes "significant authorship" and deserves a nod. Unlike the ridiculous Elanor Rigby controversy where simply playing the song with rocked up guitars somehow trampled on the toes of some obscure band who (were in a long line of obscure bands who) also played the song with rocked up guitars?? Pfffft.