My compliments on getting photos at the accident scene.
I would make sure you have your story clear regarding where you are coming from and where you are going to, to indicate your intended direction/lane of travel. These kind of claims always seem to turn up disputed when the person changes their story and says that you changed into their lane, thus reversing the alleged facts of the accident.
Let us know how things turn out and pursue the claim to get a new tire. Meanwhile, I would also make sure you request a 4 wheel alignment just to make sure no suspension damage.
Good Luck!!