I think what mathemajician means is that if the stream of data is random (in that the bits are independent random variables each with probability 1/2 of being 1) then Solomonoff induction converges on the uniform measure with high probability (probability 1, in fact).
I'm sure you knew that already, but you don't seem to realize that it undercuts the logic behind your claim:
The universal prior implies you should say "substantially less than 1 million".
You're about to flip a quantum coin a million times (these days you can even do it on the internet). What's your estimate of the K-complexity of the resulting string, conditional on everything else you've observed in your life so far? The Born rule, combined with the usual counting argument, implies you should say "about 1 million". The universal prior implies you should say "substantially less than 1 million". Which will it be?
EDIT: Wei Dai's comment explains why this post is wrong.