Well, the proof is perfectly valid, as on some abstract level a computer == Turing machine == something you can reason about. If you can prove that your program works in the required way, then your proof holds.

However, brute force solutions are ugly and shed little (if any) new light on the problem, and in the words of G.H.Hardy - "There is no permanent place in the world for ugly mathematics". With things like this I just can't help but think that an elegant and enlightening proof will unexpectedly pop up some time in the distant future when we're all off researching some sort of new-age hypermaths or something...

... well, I suppose a man's got to dream, right?