Seems as if my issue may be Mac-specific.
Here’s a thread in the official Blizzard Forums started by another person questioning the legitimacy of the e-mail.
Here’s the blue response:
Thank you for providing us with the header, Thewilly. This is a legitimate invitation; however, it appears as if the game was not properly applied to your account. Accordingly, I encourage you to e-mail email@example.com letting them know so that they can help get you into the Beta as soon as possible. 🙂
Well, hopefully it is a legit invite, but I still suggest everyone err on the side of caution when receiving any supposed beta keys.