Minjin,
Well, the proof is really in my experience with positioning of transverse filament lamps (such as the A2 lamp) in parabloic reflectors with moderate to low divergence. I am responsible for the focusing/potting of the TigerLight Gen 4 lamp module, and in the process of trying to nail down the exact position of the filament inside the spun parabolic reflector, I got to experience a lot of different degrees of focus. If you make the hotspot perfectly round you have less throw--significantly less, in fact. And if you go for the most intense center of the hotspot, regardless of the shape of the hotspot, you invariably end up with an oval hotspot, and also in the process, the focus that gives you the longest throwing beam.
So, the proof comes from my practical, empirical experience.
Mostly.
I also have a theoretical reasoning, I think, but I admit that I haven't really worked it out with ray tracing and all that. In short, the filament is not a point source; it's a line source, and its radiation pattern is actually strongest radially outward from the axis of the filament (i.e. the rays going out perpendicular to the axis). The radiation directly out from the ends of the filament (i.e. parallel to the filament axis) is significantly less, not to say non-existant. So if you think about this cylinder of light radiating outward, and downward towards the reflector, you should be able to convince yourself that if the center of the filament is at optimal focus, that the ends will send out rays of light that will hit the surface of the reflector at a shallower angle than optimum, and thus end up wide of the ideal mark, to the left and right respectively for the left and right ends of the filament. This gives you the long primary axis of the oval/elliptical shape. Then, given that the filament has very little height to it relative to its length, you arrive at the short secondary axis of the ellipse.
Of course, I'm pretty sure that the optimal throw is not precisely when the center of the filament is at the focal point. I'm rather certain it is with the center slightly off of that, which brings the left and right rays more parallel to the central axis of radiation. Still, you actually have to chose which range you want the optimum for. If you get the most darned intense hotspot on a white wall at 6 feet away, it will NOT be the best focus for 60 or 260 feet. I set the Gen4 lamp for the best focus at between 100 and 250 feet, more or less (the potting isn't precise enough to nail it down to much better than that). And I have some other lamp modules here that give a higher candlepower reading at 6 feet, but whose throw out in the field is noticeably not as good. The Gen4 doesn't overtake the 6 foot-optimal until about 35 feet, in fact.
Bla bla bla. OK. Cutting myself off.
That's what I've got. I hope it's more or less palatable for you!