"If you can look at a result set and declare that the set is not random with absolutely no knowledge of the process by which the set was generated, then you have demonstrated that randomness is inherantly independent of process."

That's the bit that doesn't make sense. Randomness isn't independent of process.

A random process is just as likely to generate any given set of numbers within its domain as any other given set of numbers. If that set just happens to be the sequence 1-10 nothing changes, that sequence is still the result of a random process. If I generate that same sequence by a non-random process it is clearly not a random sequence.

"If you can look at a result set and declare that the set is not random with absolutely no knowledge of the process by which the set was generated"

But you can't do that...

"then you have demonstrated that randomness is inherantly independent of process."

And therefore you can't do that either.