For a more abstract example, if you generate a random black-and-white static image, it will have a bunch of (short) vertical and horizontal lines in it, simply because random pixel values will sometimes cluster into sequences that produce lines. Such a line is "actually there" - different people will see it, and you can even write code that finds all such lines. The fact that its pixels were formed randomly, without correlation between each other, doesn't change this - it just means that the line has no meaning; it's data, not information. But even so, your ability to detect such lines in a static image can vary.

In a similar vein, there's a well-known issue with RNG in games, where a straightforward approach can sometimes result in e.g. repeating the same value in a row many times, which the players immediately notice (and perceive as unfair). Which is why in many games, the RNG is specifically tweaked to keep track of recent outputs and actively avoid producing more output that would form an easily recognizable pattern.