Does a camera have to record simply because it's a camera? No.
Here's something else to consider. The Fox Den has been operating since what now?... 2004? 17 years. In all those years, how many times have you heard about this establishment in the local news? Once? None? And in all of those years, you don't think that they've experienced some sort of violence inside their establishment? Drunk or high guys, guys who feel they're not getting what they paid for, guys who are being too physically aggressive or sexually forceful? I'll bet it happens more often than we know. And yet we hear nothing about it in the news. Why? Because they value privacy and discretion as much as their clients do. If they put it out there that personal information is recorded and given out when trouble happens inside their establishment, their business is over, whether or not those men deserved to be exposed. Something like that simply isn't good for the kind of business they're in.
Again, you can believe what you want to believe. But don't assume that they don't value your privacy, because they have as much to lose as their clients do. And certainly more so than other establishments, since CF and their employees have business licenses specifically for escorting.