Forty-three-old Wesley Brownlee is charged with 3 murders, but another 3 killings are believed to be linked to the accused gunman.
Five of those killings occurred in Stockton, the other in Oakland.
Both the district attorney and the Stockton Police Chief have made public statements both before and after his arrest.
Brownlee's attorney Allison Norbert argued to have future statements to the press banned.
"And that is what's at stake your honor, my client's right to the presumption of innocence."
Deputy D.A. Elton Grau called the protective order "overbroad."
"The order that the defense has created will chill the ability of law enforcement to continue to investigate this case."
With the denial, Brownlee will return to court November 14th for further arraignment.