Just read news that TrainingPeaks is now parsing .fit files for completed Strava segments on devices which supports Strava live segments, maybe this would be a cool thing to look at in GC as well. See
http://www.dcrainmaker.com/2016/08/trainingpeaks-adds-strava-segment-integration.html . I haven't looked into exactly what information that is in the file except for the segment name that Ray mentions, I hope that it's some timestamps or something else as well which should make it semi-easy to integrate.
If anyone has a .fit file from a device capable of strava live segments, and where you are sure that you triggered a segments, it would be awesome if you could post the file here.
Cheers,
Erik