This statement is false as it stands. For example, randomly taken measurements on two sets of trees gives us an idea of how tall one set is, whereas a non-random could be chosen to take the tallest of the smaller set and vice versa. Clearly, randomizing allows these sets to be distinguished.
Could you explain what you are trying to get at. (Also give us some idea of what you think is meant by randomness.)
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."