. . . tornadoes were the result of updrafts. That you then have a rain of debris elsewhere. I have heard of debris raining down after a tornado. One theory I heard was that the swirling motion starts when an updraft pierces through an air inversion and starts the swirling motion aloft. This is consistent with the wall-cloud effect.
If it were driven by the downdrafts, you would, I think, have ice and hail sprayed out of the bottom of the vortex. You should see a trail of large hail and cold rain that was sprayed like a fire hose from the bottom of the vortex. That's not what's seen. What we see is the funnel in one place and the hail in another. This suggests that the updrafts are what we find within the funnel and the downdrafts are found where the hail comes down.
Another thing, if the funnel is started by a downdraft preceding the updraft, people on the ground should notice that downdraft building.
When you say that the air below rushes up to fill the low pressure, I must point out, the air above is already at a lower pressure in every situation. This should preclude the air above forcing itself into a downdraft below. Therefore, the air above can't actually start the process. The updraft can. So, it seems to me, it would be a matter of an updraft and an inversion aloft.
I would be careful about judging the process by the aftermath. A tornado is a chaotic situation, which leads to a lot of counter-intuitive results. A cautionary tale would be forensics investigators and arson. Recently, laboratory science has proved that many presumptions forensics experts made in investigating fires were incorrect, and this led to innocent people going to prison.
You're not going to have a situation like that misjudging the origins of tornadoes, but the lesson applies that human intuition is often a poor guide as to the results of a turbulent, chaotic phenomenon. You can't put together the anatomy of a tornado from the wreckage you find afterward.
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