Not a lawyer and I don't know anything about San Francisco laws, but I'm a former police dispatcher and I've worked in the insurance industry.
Burglary is usually just breaking and entering plus some other crime. Breaking (the legal term) doesn't actually require anything be literally broken to gain entry (i.e. theft or duplication of keys and lockpicking still qualify), and you can still "break" into rooms of a home you've been invited into in some jurisdictions; so if you were not explicitly permitted into an area and a reasonable attempt to prevent you from entering was made (closed door, locks, gates, etc), it's breaking. Not all jurisdictions require a theft to occur for burglary to have been committed, there's a multitude of crimes that might qualify: kidnapping, assault, battery, rape, arson, theft, vandalism, and others might all be valid secondary crimes that would create a burglary and some places don't even require that, the mere act of breaking and entering is sufficient.
Going through someone's document may not be criminal, but copying the documents is probably criminal identity theft and that in tandem with them being in a locked away closet would probably add burglary to the charges even though the host had invited the guests into the house. From the original post's description of events, there'd still be felony vandalism and felony theft too, although if she actually reported to the police that she had essentially sublet her apartment through AirBnB, she's most certainly exempt from making insurance claims that would make her whole again.
Burglary is usually just breaking and entering plus some other crime. Breaking (the legal term) doesn't actually require anything be literally broken to gain entry (i.e. theft or duplication of keys and lockpicking still qualify), and you can still "break" into rooms of a home you've been invited into in some jurisdictions; so if you were not explicitly permitted into an area and a reasonable attempt to prevent you from entering was made (closed door, locks, gates, etc), it's breaking. Not all jurisdictions require a theft to occur for burglary to have been committed, there's a multitude of crimes that might qualify: kidnapping, assault, battery, rape, arson, theft, vandalism, and others might all be valid secondary crimes that would create a burglary and some places don't even require that, the mere act of breaking and entering is sufficient.
Going through someone's document may not be criminal, but copying the documents is probably criminal identity theft and that in tandem with them being in a locked away closet would probably add burglary to the charges even though the host had invited the guests into the house. From the original post's description of events, there'd still be felony vandalism and felony theft too, although if she actually reported to the police that she had essentially sublet her apartment through AirBnB, she's most certainly exempt from making insurance claims that would make her whole again.