AirBnB has told me absolutely nothing, except that they are acting under a regulation known as 6050W. So I researched that, and replied this to AirBnB:
The rule you referenced, 6050W, which can be found online here: https://www.irs.gov/irb/2010-43_IRB/ar08.html, specifically states, in part "Participating Payee—Foreign Address Exclusion
Section 6050W(d)(1)(B) provides that, except as provided by the Secretary in regulations or other guidance, the term participating payee does not include any person with a foreign address (the “address rule”). The proposed regulations did not exclude persons with foreign addresses from the term participating payee, although the proposed regulations did provide that in many cases a payment settlement entity may rely on a foreign address to avoid reporting. Specifically, the proposed regulations provided that a payment settlement entity that is not a United States (U.S.) payor or U.S. middleman may rely on a foreign address for a participating payee to avoid reporting as long as the payor neither knows nor has reason to know that the payee is a U.S. person. The proposed regulations also provided that a payment settlement entity that is a person described as a U.S. payor or U.S. middleman in §1.6049-5(c)(5) is not required to report payments to payees with a foreign address as long as, prior to payment, the payee has provided the payor with documentation upon which the payor may rely to treat the payment as made to a foreign person in accordance with §1.1441-1(e)(1)(ii)."
It meant nothing, they said I must supply them with tax information. Which I would happily do, except the three forms listed on their website do not apply in our situation. We would be happy to file form W8-BEN-E with them, and have actually sent them that form. They did not acknowledge it, and simply continue to tell us that we must file our tax information with AirBnB. But I am not going to falsify a form to do so.
For the record, if someone has only a phone number in the US, and/or a bank account in the US, I have already found guidance from respected tax specialists that having one or both does not subject one to US taxes or withholding.