The Captain realized after T'Kuvma lied (in accepting the Parley then killing the Admiral) that Burnham was right about one aspect of this encounter - standard Federation diplomacy wasn't goingg to work here and the Captain also realized that while Burnham did the wrong thing, she did it for the right reason (IE Burnham felt it was the only way out that could save the ship.)I'd have to rewatch, but is there a reason Georgiou let Burnham go with her to the Klingon ship instead of just confining her to a locked room?
^^^
On that score they were BOTH wrong as nothing (not Diplomacy or a 'Vulcan Hello') would have changed this as the encounter was staged and setup for ONE purpose - to start a war.
Thus the Captain knew she could count of Burnham for this particular mission. What I don't understand is: IF they had the ability to Transport more people at the same time; why didn't they take a larger compliment to board the ship a capture T'Kuvma?