She
does hire song writers.
She just pays them enough to agree not to be credited. This is known as a "Ghost writer"
THE AMERICAN SOCIETY OF COMPOSERS, AUTHORS AND PUBLISHERS is responsible for listing everyone that has written, produced or published a song.
Here's the link:
https://www.ascap.com/Home/ace-title-search/index.aspx
All you need to do is search "Bad Romance" and the original song writer appears.
It's interesting how lady gaga hasn't credited the person that actually wrote the song, Brian Smith. Instead she credits the haus and her own in house producers.
It's not at all surprising that lady gaga would need ghost writers, if you look at her song writing history that her fans love to inflate she's only written 3 songs totally alone in her solo career. A song for the PCD and a filler on a Britney Album.
I realise it's hard for her fans to accept this but her greatness as a song writer hasn't manifested itself yet.
God only knows how many other songs (like bad romance) she's purchased or paid writers to remain ghosts.