Most of those non-New Orleans jazz musicians in the earliest years were inspired, referencing, copying or collaborating with New Orleans musicians. Even in Europe, a musician such as Bechet very early on was a force for jazz on that continent. If we are talking the earliest of jazz recordings and references, New Orleans seems to dominate.
I'm not making any big claims for New Orleans itself, but I do believe this is a big reason why that city is cited as the genesis of the genre.