When Facebook first started out, it was a social network that connected you with people who went to your college. What you were signing up for when you friended someone, at least at the time, was pretty clear. You could justifiably say that if the functions and features of the application is consistant, you might not even need privacy features. When connecting means that other people can see my stuff, I manage my privacy by managing my connections--I decide upfront whether or not you are someone that I want to see what I'm posting, because I know what a post is and where it goes.
That was and has been the nature of Foursquare. Foursquare has been very consistant about what friendship means in their application--people can see where they check in. You can check in off the graph, but that seems kind of silly and isn't a mainstream activity. Not surprisingly, with a consistant sharing policy, there hasn't been that much discussion of Foursquare privacy--other than what's visable on the web and how it tweets who you are with. If you don't want people to know where you are, don't friend them on Foursquare--simple as that. That's why my Foursquare graph is about a third the size of my Facebook graph--clearly I don't need everyone knowing where I am, nor do I care where everyone else is.
It's when the application changes, like when the Facebook newsfeed launched or when people who weren't at your college could see you, that things go awry. When the features chaged, you got stuck in a situation where you weren't exactly sure the people you brought to this party when it was a dance party were the same people you wanted in the room when it became a key party.
A lot of applications are using Facebook Connect as a way to help users discover their friends and start sharing, but I'm not sure they've all considered the implications of borrowing from that broad social graphs. PicPlz seems to use Twitter or Facebook--I can't even remember how it's friending me with others automatically and figuring out who I'm following, so I'm a little more careful about which pictures I put up there.
It may feel annoying to have to refriend or refollow folks on a new social application, but getting people to do that might be worth it to ensure quality and gain trust from your users. You can always use Facebook Connect to help me identify who I might want to follow, but I don't think graph recreation is a bad thing. That's why I never liked Friendfeed--because who I want to connect with around different functions on the web is nuanced, and I didn't like the one graph fits all model for sharing.
Startups might think that the more friends someone has on their site, the better, but I'd be more focused on engagement. GroupMe was the smallest of all of my social graphs, but it was a high engagement platform that I participated with the people I see most. That's just as valuable as adding a bunch of people I don't care about for functions that may change in the future. The more uncertain I am about the consistancy of the future feature set, the more I'm going to be hesitant to engage on the platform for fear of the privacy rug being pulled out from under me.