What if an app you download does the paid/free split with previously free downloaders getting the paid version for free via the update?
I've had that happen before, and that was the right way to do it. If you don't tie the free downloads to the Apple ID, there won't be a way to determine you've downloaded the free version in the past.
I suspect that the free download is still tied to your Apple ID. Not having to provide a password each time shouldn't change that. I'm assuming you have to be logged in to the store (with your Apple ID) in order to download anything at all, but I frankly haven't tried it yet on iOS 6.