In the US, in my experience, I'm about 50/50 in getting charged for tire damage vs not being charged for tire damage.
In all of the situations, I probably should have been charged (hitting curb, hitting pot hole, etc) though when I return the car after calling AVIS Roadside Assistance, I've simply told them I had a flat tire.
One time I shredded a tire side wall by scraping up against a curb. There's no way this could have been repairable, and I was only charged $40.
TL;dr...
Its totally random if you get charged