That is indeed the core of the argument. There are good reasons to see it from either point of view. How does one distinguish between a rule or regulation that provides a public benefit or prevents a public disaster with one that merely infringes on liberty without an overwhelming public reason to do so?
There has to be a clear definition on what elements are required or should be required by law to run the business and there usually are. For instance, in Washington state, we are required to retain applications, reports and all other tenant files in a secure location, in some kind of locking filing system. The only time this would be inspected, however, if there should be some kind of problem or suspected problem as to privacy.
Of course, if this is kept in the home, then we would have to let someone in to see it. This is where having a secured office separate from the home is quite beneficial because you only have to let them in to the location where the operations of the business are conducted. So if you have an office separately located in your garage or a separate storage shed, this is most beneficial because you can't be required to allow them into a structure that has nothing to do with the business. Makes things easier, too - any cleaning products, paint, maintenance supplies and equipment for a home rental business can be stored in a shed and separate insulated and locked room can be used for an office or even just for file storage.
Some of this also has to do with the type of business - a corporation, an LLC, etcetera.
If the mandate is that regular inspections be done, then there must be a delineation of where they can inspect and where they can't and he should be prepared. If they have the right to inspect the entire premises ... well, I would take issue with that and lobby to have the law changed to comply with the constitution. I would also seriously consider a structure separate from the home in which to conduct business.