So the title is nonsense and there was no proof at all?
No. 'Fair' doesn't really mean 'Random'. 'Fair' means that there is no hidden mechanism implying lying about the past.
Say you want to play rock, paper scissors (RPS) with a machine. You can not just chose R, P or S and wait for the machine to tell you if you have lost or won. A fair way of doing this would require that the machine shows you a hash of a salted R, P or S world. Then you chose R P or S and the machine shows you its initial salted phrase which was beginning by R P or S. Therefore you know that the machine did not lie.
A machine could very well not be random and still be fair. If for some psychological reason people tend to chose rock as a first bet, the machine can very well be programmed to have a tendency to play Paper as its first bet. It would still be fair as long as the machine does not change its mind when it notices that the player actually played scissors.
In the same way, it is very well known that people really suck at picking up random choices. So the machine could try to detect a pattern in the player's choices. And still, it will be fair as long as the machine doesn't lie on what it picked before the player actually bet.
Actually, it is much better to play against a machine that is not truly random, because it is
predictable. So people can carefully study how the machine behaves and try to deduce its algorithm. So, fairness has very little to do with randomness, imho.
I hope this all makes sense to you, but I confess it's tough to explain. It's probably easier with an example:
Human: Let's play Rock, Paper, Scissors, shall we?
Machine: Sure, let me think of a random number...
Machine: Ok I got one. The sha-256 of the string I'm thinking about is:
50a32f4b3864165afb1d52f709191e7eaf98c9dfca572b9406a9110759b24aa3
Human: Ok.... PAPER!
Machine: You win. My initial string was: "ROCK 59496.1637704731"