Most false documents can generally be detected by reference checks, particularly if it includes a credit check. The landlords in the article did not sound like they'd bothered.
Property ownership is not trivial to check: not only does the registrar vary by location, with varying availabilities of information, but who is to say that person X asking airbnb to do / not do something is the X on the title? Further, lots of rental property is owned by a LLC/trust/corporation. Of course you can determine who is authorized to speak for the aforementioned LLC, but it's not an api request away.
Property ownership is not trivial to check: not only does the registrar vary by location, with varying availabilities of information, but who is to say that person X asking airbnb to do / not do something is the X on the title? Further, lots of rental property is owned by a LLC/trust/corporation. Of course you can determine who is authorized to speak for the aforementioned LLC, but it's not an api request away.