"What was the flat due to? Puncture (nail/glass/etc), you hit a curb, tire worn out, other? That will ultimately determine the liable party."
Don't think so. It's the norm in Europe that if you incur tyre damage (no matter how or why), you pay for it. It isn't considered fair wear and tear over here.
If you drove some distance on the flat (which may be unavoidable on an autobahn) you've probably ruined the sidewall, so a repair isn't viable.