I wouldn't know. There is not much info available in the public about the game mechanics before Blizzard took over. What I wrote is true, though, that has been said by many current and former Blizzard employees.

It's always been my understanding that the publishing deal was struck early in development, but the actual acquisition was done almost at the very end.

I'm aware that it was originally going to be turn-based, although I'm not sure at what point in development the shift happened.

Off Topic:

So after Heart of the Swarm, whats Blizzard gonna release afterwards?

My wording was bad, you are correct in saying that we don't know when exactly the change happened, but it sure did happen thanks to Blizzard. I think this was mentioned in one of the Anniversary videos.
The ones we know about:

Hearthstone: Heroes of Warcraft will be released late this year, or early next year, this is certain.
Legacy of the Void is still far away, my bet is that the expansion will be released in late 2014 or early 2015.
Project "Titan" was pushed back to 2016 at the earliest.

The ones we don't know about (personal speculation):

Diablo 3's first expansion may be announced at BlizzCon 2013, possible release in late 2014.
WoW's next expansion may be announced at BlizzCon 2013, possible release in mid 2014.
Blizzard All-Stars may be officially announced as a standalone free-to-play title at BlizzCon 2014, with a possible release somewhere in late 2014 or early 2015.