Really, it seems like turn-key services are the primary solution, though the important thing is to get a competitive marketplace where some are ad-supported, some aren't, but all of them are reasonably trusted.
Diaspora server will be the same. Your random 419 scammer won't be able to make a lot of friends if people are a little careful. Add PGP keys and a proper web of trust, and the scammer won't be able to spoof any identity at all.
That said, would it be possible to get research universities to act as the network? I assume people would be trusting of that.
Or is there a way to encrypt data or split it up in ways that makes it meaningless to any individual without the right password/signature?
There are ways to combat this. Using OAuth for authentication keeps them from getting your credentials. It or a similar protocol for data exchange allows you to shut them off if they're proven bogus. They might have limited visibility into your network in the meantime, but that's it.
It will probably end up working a lot like the web works now. You'll have to look at the URL and decide if you trust the provider. You can also send a message along with the friend invite and prior to accepting another's invite, that gives you some confidence that you know that person. Finally, by seeing that you share common friends on common providers will be a strong indicator.