I just got off the phone with San Diego State, and the word is: I have been officially admitted for the Fall of 2008. I'm going to grad school!
Back on May 9, I had already received an e-mail with the same subject line as this post, with a qualification attached: that I had been recommended for admission by the School of Business but that official admission could only be granted by the Division of Graduate Affairs. It went on to say that I could expect a further update in about a week.
Having not yet received that update, I called the Business School a few minutes ago. They are re-sending my paperwork to the Graduate Affairs office, and explained that this final step is a formality, and that I can plan to begin classes in the fall.