You can only access the training area if you have the quest to find the missing Selkath active. To get it you'll need to talk to the Selkath named Shaelas in the Mercenary cantina before entering the Sith base. It is located on the other side of Manaan than the Sith Embassy.
I think it is possible to get aquited at the trial after you exit the Embassy even without the evidence from the training area but I don't remember the correct dialogue choices for it. If you get the right choices you can return to the Embassy later through the Sith hangar bay to look for the missing Selkath.