The rule against third party bookings applies to guests, not to hosts. Here is the wording in the Airbnb Terms of Service:
"You understand and agree that you are solely responsible for compliance with any and all laws, rules, regulations, and Tax obligations that may apply to your use of the Site, Application, Services and Collective Content. In connection with your use of the Site, Application, Services and Collective Content, you may not and you agree that you will not: unless Airbnb explicitly permits otherwise, request or book a stay at any Accommodation if you will not actually be staying at the Accommodation yourself;"
I accept third party bookings. Several times I haven't known it was a third party booking until the guest arrived. Once I didn't know until half way through the guest's stay.