Privacy is more of a responsibility than a right because it's not an explicit right. It tends to appear as a manifestation of all of our other rights, without ever being actually granted as a right.
For example, if you own property, the law is that other people can't trespass on that property with your permission. That means that even though you don't have an express right to privacy, what you have and what you do on that property becomes private knowledge that only you and your invitees know. Furthering this idea is the fact that even the government and law enforcers can't come on to your property without either your express permission or an official judicial warrant that's only issued if there's a demonstrated probable cause that you're doing something illegal.
Privacy also ends up being somewhat implied by people's right to speech, religion, and so forth. If you're allowed to express unpopular opinions -- and that's even a protected right -- then surely you're allowed to have unpopular thoughts. Your own thoughts, opinions, viewpoints -- anything you think, say, and do that's not illegal -- is your own private viewpoint unless you make a public spectacle out of it. You have a right to privately hold whatever beliefs you want, and even to express them to your chosen audience. Same with religion. What faith, or lack thereof, you choose to practice is up to you.
An implied 'right' to privacy also comes about historically, such as through the abolition of prohibition laws (drinking becomes a personal, private decision, as long as you're not doing anything illegal), and more recently in modern history (women being granted a right to a quick and quiet abortion - even married women terminating pregnancies without their husbands' knowledge, and even minor children doing so without their parents' knowledge in some cases). Homosexuals being granted the right to marry (previously stigmatized sexual practices becoming a legitimized private personal choice). And so on.
Essentially, without actually saying it out loud, the rights people have been given, initially and over the years, paint a picture that unless something is specifically illegal, anything people say, do, or think is their own business. It's private unless they make it public.
I would think marriage is a public matter.... But that misses the point.
If more than 3 people are aware of some given information, all people aware of that information should assume it is not private, and the world knowing is outside of their control.
From my point of view, the "right to privacy" would be akin to the "right to bear arms". It does not mean anything if it is not exercised. In other words, no government gives people rights to "bear arms" or "have privacy", the people who care enough will exercise the responsibility of obtaining such abilities.
Well, that's every right the government grants. A government-granted right is essentially the government saying, "we won't stop you from doing X".
Anyway, I think your definition of privacy is a little stringent.
If I am required, by law, to disclose that I am doing activity X in my home, with some kind of penalty imposed if I fail to disclose my performance of activity X, then that's not private. I have no choice whether people know what I'm doing in my home.
But we have the opposite situation. It is illegal for anybody to come into my home without my permission. Even the government and law enforcement officials. Therefore, anything I do in my home is private.
Sure, I could tell three or more people what I'm doing, but that's my choice. I control who does and does not know what's going on. It's my information to disclose or withhold as I see fit. So it's private information. If I'm really worried about it becoming less private, I can even have people sign various contracts not to disclose the information, which imposes a penalty on them if they don't maintain my privacy.
If I control the disclosure of the information, then it's private information, until I choose to make it public.