Apparently there is only 1 client to install the game (no distinction between starter/standard)
On the 15th, logged in to battle.net and entered the standard account. I can clearly see the the copy of Diablo 3 as "Standard Edition".
Launched the game, logged in and can still see the "Upgrade banner" on the top right. Went all the way to the black king, and as soon as I did the last blow, I got a big dialog prompting me to upgrade.
Did download the client again, installed second time, no dice.
Completely removed the game, installed from the hard copy DVD that I bought, still getting the same "upgrade now" banner.
Haven't been able to find a similar post, which makes me wonder if I'm missing something. Did send an email via the "Customer Services" option within the game and awaiting for a reply.