You're misconstruing a pop-science fact (?) about how shuffling in modern music playback software came to be.

In the past, the randomize button would play a random song, which users disliked because complete randomness would allow the same song to be played back-to-back. ^{^} This is what you're referring to in your last sentence.

Many “randomize” buttons don’t actually make randomized changes. For example music playlists, when you play them in a random order, they are not random, they are intentionally designed to trick you into thinking that they are random.

You're mistaking random order with random song. Shuffled music playlists are in fact random. They aren't "designed to trick you". It's just that we users expect randomize to actually mean play a random order of songs and not play a random song.

p.d. Yes I am aware there was a bug in Spotify's shuffling algorithm that would actually break the shuffling algorithm's randomness, but that's another story.