I think it's not only an apparent conflict of interest; it's a real conflict of interest.
That's not all that the IAG does. When you come to the ministerial stage, the minister turns to the same people who were very ardent and aggressive advocates in the courtroom for advice on whether, ministerially, he should surrender the fugitive. There's clearly a bias there too.
It's been recommended. It's not among my four, because I didn't come with a vast shopping list, but the truth is that it puts those people, however well-meaning.... It would put any of us in an apparent conflict of interest, and likely a real one.