I've been in contact with Airbnb over this specific issue (WiFi used for illegal downloading). Here was the relevant statement from their response:
As per our Terms of Service, we are excluded from liability with respect to loss of data or any related fines or fees, or incidental, special, or exemplary, or consequential losses of this nature. For more information regarding our Terms of Service, please see: https://www.airbnb.com/terms.
Also, if you’d like more info on the subject, you can visit: https://www.airbnb.com/help/article/827.
@John4812