From that info we can draw the following conclusion: sara lied about kaname being involved in zero's drama.
Sara came to cross academy to obtain something she want, aka a hunter. and who's better than zero who already loath PB's, specialy kaname. And if sara add some fuel to his drama, like kaname being guilty for his drama, the silver haired hunter will be afected, obviously.
In my opinion, sara's words cannot be trust. she already lied about kaname killing ouri.
Even without seeing SGK info I thought Sara is lying.
From those teasers, aparently zero believed in sara's lies and he rushed to yuuki to share this. now, we must see if she will believe this lie.
If she will believe kaname will suffer alot.
Somehow, I think yuuki will believe that lie and when she will find out the truth she will blame herself for not having trust in kaname or accusing of something this sort.
I think hino used this as a way to prolong LT - in case yuuki will believe in sara's words.
If yuuki won't believe in sara's words, then I think LT will end soon.