The camera recorded the dog walker screaming "Oh, my God! I've been shot!" and "Help me!" and "I'm bleeding out from my chest!"
Fischer lost part of a lung.
"While I'm deeply concerned at the events that led to his release, I'm confident law enforcement will rectify the error," Fischer said in a statement obtained by KABC-TV.
"I ask for Mr. Jackson to turn himself over to the authorities, so resolution to the crime committed against me runs its course, whatever the courts determine that outcome to be."
The pop star's dogs were returned two days later by a woman who claimed she had found them tied to a pole and asked about Lady Gaga's offer of a $500,000 reward if the dogs were returned "no questions asked." The singer was in Rome at the time filming a movie.
She's charged with receiving stolen property and the father of another suspect is charged with helping him avoid arrest.
Jackson already had been charged in the attack and had pleaded not guilty when the county district attorney's office filed a superceding indictment Tuesday charging him with attempted murder, conspiracy to commit a robbery and assault with a semiautomatic firearm.
The move was done "to speed up the legal process" and Jackson was arraigned Wednesday under a new case number, the DA's office said in a statement.
"Mr. Jackson was subsequently released from custody by the Los Angeles County Sheriff's Department. We are unsure as to why they did so," the statement said.