The Doctor inspired Cinna :) Kudos to this work

That's a great and totally right reason for the Doctor to leave Panem without doing anything. And absolutely right and characteristic - for the Ninth Doctor. And even if he wanted to interfere, even if he knew it would help - he couldn't, just because it's hard for him to play by this cruel world's rules. He can't - even the Ninth - he can't just "shoot them in the head" whatever he says, and that's his greatest trouble AND blessing.
I can see so many other things in this little scene. I just can't stop rereading it.
Would you mind if I translate your story into Russian? There's not many good crossovers, and I really want to share it with our non-English speaking community. Be sure, I will leave the link to your page and save your authorship.

I wish Nine would learn this on Satellite Five! I miss him!

When has he ever shot anyone in the head? Ever?

Love Cinna! Love the ninth Doctor! :)

I don't necessarily agree with the Doctor here - he could stand around, give the right nudge at the right time - but it is in-character for Nine. Just write a sequel where he saves Cinna, please... Just Cinna...