If you do some reading around MVP, you might be surprised at what a low standard exists to constitute a product. Some folk even count an ad + landing page as an MVP. ie. 0 code base. An MVP is a point of departure, not arrival.
I will certainly concede that, especially given that this isn't anywhere near my realm of knowledge - I'm strictly a coder and don't have the vision or insight into product presentation, preparation, or anything like that.
However, my instinct tells me that the example you mention of say, an ad + landing page, IS an MVP in one good sense - to gauge interest in a potential product (an iPhone app, etc), gathering subscribers to mailing lists, beta signups, etc.
But in the scope of what Diaspora is trying to accomplish, releasing the code base like this doesn't qualify as a product - I think.
I am way more than willing to be wrong on this point, though. I'm also probably just splitting hairs by this point.
At the moment, their primary task is actually to gauge/encourage interest - without that, they have lost.
A following task is to discover if what they have is usable/useful by real people, and the only real test of that is to release it and get feedback. Related is flushing out bugs (most effectively done by actual usage); testing performance (even for small numbers of users); and of course flushing out specific privacy and security issues. Note that it's not actually necessary to even continue with the same codebase; it is possible to use it as a prototype.
I think a helpful way to separate a "product" from a "codebase" is to ask whether a complete rewrite in a different language with a different internal architecture (and of course codebase), that is indistinguishable to users, could be sold as the same product.
I think the Mythical Man Month would be of interest to you; he has your perspective, but with a wider scope. I think you'd really enjoy it, if you haven't already. Some fascinating ideas appear right up in chapter 1, very clearly written.
It's fun to think of a software product as a giant ADT (Abstract Data Type), as it specifies operations that may be carried out (via a GUI, or command line, or webpage, or webservice, etc), while the detail of the implementation of those operations is hidden. Each instance (running copy) of a software product contains its own data.
