I think it is possible to pay for independent advice without it being biased. I give such advice for my job, and while I "help" the client as much as possible, ultimately I am beholden to the code of practice of my professional organisation. So if the client asks me to audit/ assess their "final product" without having taken on board any of the preceding advice, it will be a "bad" review that won't get them what they need (and I'll tell them that and make further suggestions as to what could get them over the line!).
But it sounds like Hamilton hasn't been asked to provide "advice" as such, but make a judgement on whether or not a line has been crossed - without my safety net of being able to say, "well, that's crap, but if we add this to your final product it will be less crap and I'll redo the assessment for you". He has to assess what has already been done, and that assessment could have real and immediate consequences that can't be dealt with by changing a policy or tweaking a process before the next audit. I imagine that's far harder to do truly independently when the person who appointed you has, literally, their job on the line. So it does seem an odd way of establishing an independent review.