We'll at least likely see Heart Containers in dungeons, since there are (according to that 'accurate' rumour) at least four big dungeons scattered around the world. Presumably these have both major boss battles and Heart Containers as rewards for winning said boss battles.
I also suspect they'll exist as rewards for clearing the optional shrines. I mean, we're supposed to have about a 100 of them, right? Well, we certainly aren't getting 100 runes in this game. And getting something trivial like clothing or weapons seems very unlikely. So perhaps the extra shrines all have one piece of heart in them. That would add up to about 20 something hearts, which is fairly close to the standard amount in a Zelda game.
Then again, maybe the dungeons don't just give us one extra heart. Perhaps instead, they give us three or four extra hearts each, like how the new Paper Mario game gives you 25 more HP for every boss beaten. That's possible too.