The only way to dispute that would be appeal to authority so I will avoid. Perhaps there was a time when he did identify as a mathematical/theoretical statistic

The only way to dispute that would be appeal to authority so I will avoid. Perhaps there was a time when he did identify as a mathematical/theoretical statistician, but his contributions were quite a dramatic break from what was the norm in statistical practice at the time. I would argue that his contributions were central to the birth of rigorous machine learning (the non deep learning kind) as a field of its own with a focus that's different from that of statistics. One quantitative test I can suggest -- one can count the number of occurrences of the word 'statistics' in the journals and conferences he has published and compare that with the number of publications he has authored. My sense is that it will be close to 0 and getting closer (if not already there yet).