Your point is focused on the subject of observation. Mine point is focused on the object, just as the universe is the object of human observation. Unless the object is distinguishable from others of its kind, random tests will produce no results. A non-random process must in some manner or to some degree, comprise one or both objects.
When I use the word "randomness" I mean "having no specific pattern or purpose."
If an object isn't distinguishable from others, no test will tell them apart, with or without a random component. This has nothing to do with your original statement.
"having no specific pattern or purpose."
Again partly false. I often generate "random" objects with various purposes in mind: cryptography, un-biased selection, etc. The phrase "specific pattern" isn't well defined; any given pattern will occur with probability one in a random environment.
Humpty Dumpty smiled contemptuously. `Of course you don't -- till I tell you. I meant "there's a nice knock-down argument for you!"'
`But "glory" doesn't mean "a nice knock-down argument,"' Alice objected.
`When I use a word,' Humpty Dumpty said in rather a scornful tone, `it means just what I choose it to mean -- neither more nor less.'
`The question is,' said Alice, `whether you can make words mean so many different things.'
`The question is,' said Humpty Dumpty, `which is to be master - - that's all.'