They probably would have been interviewed together initially. She was split off later and interviewed separately. I believe the PD did that when they were called in.
The PO would have initially tried to figure out who all these extra people were and probably questioned them together. The scenario would play out with them becoming more defensive and further arousing suspicions. At some point they probably clammed up and starte demanding lawyers, at which point the PO called the cops since it was obvious that something that they were hiding something. I am guessing that is what PG is referring to.
Here is an account from the interview in the San Jose Mercury News
http://www.mercurynews.com/localnews/ci_13240607?FORM=ZZNR9
At first, the girls and woman seemed reluctant to answer basic questions asked by the parole agent and Concord officers while the Garridos were in the room. So the officers separated them.
"They weren't suspected of anything. It just didn't sit right," Lardieri said. "The suspicion was so high that we couldn't just leave this as it is."
In a room by herself, Lardieri said, the woman now known to be Dugard quickly admitted to her real identity.
Lardieri said he suspects that it was the first time she had come under serious interrogation and she succumbed to the pressure, implicating Phillip Garrido as her kidnapper.
"Through some additional probing "... s
he finally confided and said, 'This is what happened and this is who I am,' Lardieri said.
Garrido was immediately jailed at the Concord Police Department on a probation violation. Dugard and her two daughters, meanwhile, were questioned further by El Dorado County cold-case investigators, who happened to be in Stockton and headed over once they got word of Dugard's reappearance. A short time later, Nancy Garrido was arrested.