Oh but it is, Sidious is giving more and more power to the military in the name of 'security' - at this point the Republic is half way to becoming a military state, the military have more power than the Jedi, and they can do what they want. And by this stage Tarkin is becoming Sidious' personal protege, Sidious made many of his 'friends' who would later become the leaders of the Empire, during the Republic era - Tarkin, who is now an Admiral, is the chief of these. He and the Chancellor and likely working together.
So it's his responsibility to show the evidence. If Tarkin could not show the surveillance camera record during the escape and the sound during the interrogation then there's clearly something going on. It's not the Empire era yet, nor was Tarkin the sole leader of the military, he was not such figure even in the Empire era. The Senate and the Chancellor could all be used against him.
But of course they'll show evidence, it will just be faked. The Jedi don't have enough power to challenge the legitimacy of it. Although its clear that they're not completely convinced.