@Donald28:
In actuality, you are running a business when you regulalrly provide a service or tangible good to another individual or entity for money or other payment. While Airbnb may seem small to you, it is a regularly offered service in exchange for a payment. I can't speak to Douglas County, but here in AZ our county sends me a list every year that I have to complete listing all of the items in the home for both my short terms (STRs) and log terms (LTRs). Of course, my STRs are taxed more because there is furniture inside them as opposed to stove, fridge and dishwasher in the LTRs. STRs inside the city limits require a business license while the LTRs don't.
But regardless of the local laws, you should be operating as an LLC and as a business simply to protect yourself personally in the event of a lawsuit. Normal homeowners insurance will not cover your guest's injuries or the lawsuits they bring against you. Some homeowner's insurance will immediately cancel your policy if they discover that you have an STR on the property. If you read the Community Center for long you will find that Airbnb's advertised insurance policy cannot be counted on to protect you either.
That got a little bit off-topic to your post, but what you are experiencing with Douglas County is not unusual.