In Terminator 3: Rise of the Machines we see this exchange:
BREWSTER: Crystal Peak. You have to get to Crystal Peak.
CONNOR: That's the system core?
BREWSTER: It's your only chance.
So general Robert Brewster believed that "Crystal Peak" is the Skynet core? Being the leader of Skynet programme, How did he misunderstand the core structure of the project?
General Brewster was very well aware that Skynet wasn't housed at Crystal Peak. He was telling John to go there because it was the nearest hardened facility that would survive a nuclear strike, and hence would protect his daughter.
The room was getting dark. It was becoming hard to focus on anything. He felt a deepening flutter in his chest that frightened him. "Crystal Peak," he muttered. "You have to get to Crystal Peak."
...
"That's the system core?" Connor asked the general.
"It's your only chance," Brewster said, his voice now barely a whisper.
John, obviously, misunderstood.
"Goddammit, there's nothing here!" He looked at Kate and nodded beyond her to the lobby and the elevator that had brought them down from the tunnel. "Why did he send us down here to?"
"To live," Kate said softly. "It was his mission."
Connor shook his head and lowered his eyes. He was spent. It was all over. "There was never any stopping it," he said. The detonator fuse was counting down. Less than one minute to go.
As an aside, The T-X recognises that the facility (coincidentally) offers a unique opportunity for John to harm Skynet by providing him with a command & control capability with radio links to every military base and enough food to last him years
If they had acquired the necessary data from General Brewster, there was a chance that the humans, John Connor and Katherine Brewster, could have a major negative impact on Skynet if they were allowed to reach the control center core. This could not be allowed to happen.
