Parenteau sent a text message to Downey on Sunday telling him a 14-year-old boy was taken to hospital after suffering a head injury at a new skate park.
Downey took to his Facebook page Sunday night expressing his sympathy for the family of the hurt teenager.
A few hours later, though, he posted an update revealing the whole thing was a hoax by the mayor.
"I have just been re-advised by the Mayor that it wasn't true and NO ACCIDENT HAPPENED at the skate park," he wrote.
"Regardless, head injuries and head trauma incidents are nothing to joke about or to make up stories about especially when you involve a minor in your story."