Apparently a European Blizz tech support dude said this:
As already mentioned, youll need a World of WarCraft or StarCraft 2 Account to participate in the Diablo 3 Beta Lottery. If you dont have one, youll have no chance to create a Diablo 3 Beta Account if you win. This applies to our forums as well.
We dont do this because we only accept paying customers for the beta, even though it might look like that.
We want to prevent that players create countless Battle.net Accounts to take part in the lottery. Because of that, only players with an activated game will be able to take part in the beta lottery.
Might just be for EU though, as both games are the only ones with current support in the continent (according to someone on the D3Incgamers comments). Assuming this doesn't apply to everyone else, I wouldn't be surprised if the Beta still requires a valid purchase of a Blizz game.