I think one thing you're missing is the idea of social validation, or social proof, of your product. Like TallGuyShort said, getting invitation emails is rather annoying, and quite insincere. Users can spot that insincerity in a heartbeat. Sure, you'll rake in some users, but what you want is to create a demand for the product. When I did that whole FluShirts thing, I used twitter to message people, and within seconds I would see them tweet "haha, check out these shirts [flushirts url]." I'm not sure as to what percentage of shirts I sold were because of twitter referrals, but what that did at the very least was introduce my product to others in a genuine manner to potential customers using their friends.
Of course, to gain social validation of your product, it needs to be useful and something people will enjoy. There are some counterexamples, like hi5, that are fairly popular and got to that point because of their random email invitations (I don't know who you are Aaron, Britney, and Alexa), and to that, I'm not quite sure what to say. I guess they found a market. But as far as virality goes, in the genuine sense, I think Facebook/Myspace/Twitter beat hi5.
Of course, to gain social validation of your product, it needs to be useful and something people will enjoy. There are some counterexamples, like hi5, that are fairly popular and got to that point because of their random email invitations (I don't know who you are Aaron, Britney, and Alexa), and to that, I'm not quite sure what to say. I guess they found a market. But as far as virality goes, in the genuine sense, I think Facebook/Myspace/Twitter beat hi5.