For one, this is a private business, not your house. If you're walking in there thinking your actions and conversations are protected by privacy laws, then you're mistaken. Privacy laws outside of "sanctuary" (i.e.: a private residence, washrooms and changing rooms, doctor's office, council with your lawyer) only extend to your personal information. Should you decide to announce your personal information or expose yourself outside of those protected areas, you F'ed yourself, and no law will protect you.
Second, you assume that a room with a closed door and closed blinds equals privacy. That would be a mistake. Except for washrooms and changing rooms, where a person is expected to expose him/herself, all other areas are within the business's rights to view. If the camera was pointing at the shower, you may have something to argue about. But the Den is technically a "body rub", not a brothel. The assumption is that no "illegal" activity is occurring in the room... That is to say, when you walked into the Den, you cannot argue that you are ignorant of the law. By walking in and paying money for a service, the law will assume that you have understood and agreed to the terms and policies of that establishment, that no illegal activity will occur as a result of your transaction. You are there only for an innocent massage... on a massage table which conveniently looks like a bed. If it were legal for you to be stark naked in that room, with a stark naked girl, doing what any adult would be doing in that situation, then you'd be protected by privacy laws.
Third, the law cares more about the women who work there, than the men who visit them. Accept it. Carman Fox has to assure all possible measures are taken to ensure safety for her girls. Any business which leaves their female employee alone with a potentially aggressive (or in this case, a sexually aggressive male) treads on very very thin ice. The girls who work there have a much better chance of winning a lack-of-safety case against the business, than you have of winning a claim to lack-of-privacy.