The first cabin was located across the street from the police command post/media briefing center. Dorner was holed-up there since Thursday. It was vacant until the owners, a husband and wife, arrived to clean it up. Dorner captured them and tied them up, then stole their car to make a break for it.
During his escape, he was spotted by a pair of park rangers, but when he broke that car, he jacked a guy driving a pick-up. He let the guy and his dog go and was driving along a dirt road when a pair of fish and game wardens spotted him and gave chase. He got the truck stuck in a ditch and fled into the cabin that burned down.
A resident who lived 4 doors down from the first cabin, also located across the street from the command post/media briefing center said no one ever came to search their house, meaning that no one searched the cabin in which Dorner was holed-up.
So, he was hidden under the noses of the police the entire time and would have remained undiscovered except for the chance encounter with the husband and wife.
Well, then, no wonder LAPD fired Dorner.
He forgot to shoot the dog.
Thanks to all of you for clearing that up for me.