I think you are mistaken.
By your theory, flipping coins is rigged too. You don't get heads, tails, heads, tails.
You get the same sort of streaks you see here at chess.com.
How? I am not talking about my own experience, like i said multiple time in the post you should check your own and random people's account winning and losing. It is always the same pattern. Even your account has the exact same patter I mentioned above, 3-4 win then 3-4 lose. And literally no win - lose - win - lose
Even in real life you get streaks. At my club I can get a winning streak against a similarly rated player and the next session, barely manage a win. Other times we may be more even.
It has nothing to do with the site's pairing algorithm. It's already complicated enough, that for them to add additional criteria to the pairing logic to try and elicit some addictive response is nonsensical.
Mine was more dramatic. I lost to a player 0-4 on a particular week. The following week I returned with a 3-0 win over the same player.
The coin flipping is normally done using 'fair coin'. They are specially minted. You can get them from specialist suppliers of maths and scientific equipment. I believe they are quite collectable and worth several times their face value.