I believe you are correct. Having listened to the scanner feed for the best part of the four days my recollection was the DFW and SBSD were on the scene with SBSD having the lead. At one point LAPD had 20 officers at the airport who were told to stand by and that SBSD had enough manpower on the scene. I never heard the LAPD officers called in.
A question one might ask is why the print media published the manifesto...leaving out not just names but also complete paragraphs. Why then say they were only removing names to protect those people? Had I not stumbled across a comment with a link to the complete manifesto I might never have known what I was given by the media was only a portion.