And Burnham was ultimately correct. Georgiou's greeting "We come in peace" was answered by a fusillade of phaser fire and a surge of violence the likes of which Starfleet has probably never seen before. It is a twist of irony that if Burnham had successfully circumvented Starfleet's lofty principals and fired on the Ship of the Dead, the Great Houses would have arrived to find T'Kuvma's ship blown to pieces at the hands of a much smaller Federation vessel and they would have warped away laughing to themselves about "That vainglorious fool with that rusty old piece of junk." There would have been no war, and no compromising of principals either, and Burnham probably would have gone to prison with a clear conscience knowing that she saved her friends and her captain and maybe the whole Federation.At the start of the show, I think that Georgiou, a human, was clearly espousing values consistent with Starfleet idealism and certainly with that type of idealism as it's expressed by Picard a century later. The Starfleet that we've seen in action since then is one fighting a war.
In fact, a major plot point in the first episode was that Burnham decided that that idealism was incompatible with the realities of dealing with a species like the Klingons.