@Carol-Lee1 I understand what you are saying, but I don't worry about that at all since I will always have the information in my Transaction History and at year end Airbnb provides a consolidated report ( Transaction History > Earning Summary). If there is any dispute, I can prove that Airbnb collected the taxes from my guests. The county would go after Airbnb, not me.
I also have a permit number since I have been paying TOT myself for many years. Personnally, I like the way Airbnb is doing it and I'm sure that the county is happy since now 100% of the TOT taxes will be paid. There were lots of hosts who never paid it either by design or by ignorance.
So, in sum, you can prove that Airbnb is paying it for you. You don't need to prove your are paying it since you are not. Airbnb is.