Mbappe has hinted at issues with Real's medical staff, which has seen a major overhaul since the turn of the year.
And Riolo, speaking on RMC, says the problems have centred around the treatment of Mbappe's knee concern.
He stated: "It's clear there was a mistake if the player decided to travel to Paris (to undergo treatment).
"I would say it's because the diagnosis of Mbappé's knee was so catastrophic, and undoubtedly worse than catastrophic, because it was a very serious error.
"And that's why they fired everyone, in addition to the string of injuries, but it was largely due to that.
"It could have been extremely serious because of a mistake. Because Mbappé spent time playing matches without knowing what was wrong... He could have torn his knee. He continued playing and saw that it still hurt, but he knew something was wrong.
"Let me tell you something. The mistake was huge, and that is that they examined his other knee. Do you think I'm talking nonsense? That's what happened. You'll understand that if you're playing with an injury and you don't know it, you can seriously hurt yourself..."
Mbappe, at his France media conference yesterday, offered more detail: "I was fortunate enough to receive the correct diagnosis when I went to Paris, and together we were able to devise the best plan to recover my best form and be in shape at the end of the season with Real Madrid and for the World Cup.
"I received the diagnosis on a specific date that I can't reveal now. But everything that had been said before was completely false. I didn't go through that period in the best possible way; I wasn't exactly the happiest player in the world..."