Re: I am still confused
He is accused of being an accessory to a crime committed by a US citizen while on active duty in Iraq. This is not just a "the USA didn't like what he did so charged him" thing, but a charge with a clear nexus to the US. Oh, and by the way, whether you like it or not "get stuffed" is not a response to the actual extradition agreement between the US and the UK. And, yes, there are real First Amendment issues to be navigated, but you can't claim the protection of the First Amendment to the United States Constitution outside the United States legal system...
And there has been absolutely no indication that the trial will not be public. You are probably confused about Grand Jury proceedings, which are confidential for good reason -- and you may choose to think Grand Juries are a bad idea (I'd agree in many, but not all, cases), but if one has the things, the evidence presented to them _must_ be confidential unless you want a rule-by-Daily-Mail situation where accusations are leveled and no opportunity to refute them is presented.