Heavy Rain is like a painting best viewed from a distance. I could run with the emotions of the moment, as though it all made perfect sense. Once you analyse the details it's clearly full of holes and falls apart.
I will certainly stand up for Heavy Rain's potential and vision. But there is something more than just that. I'm an easy target emotionally, but it wasn't just sensitive people like me who were affected. I watched friends trying desperately to overcome a stressful situation. They were caught up in the moment just as strongly as I was. There's a power to that, however easy it may be to pick on the game's flaws.
There are many flaws I can't defend, and wouldn't try. But something I believe helped my Heavy Rain experience immensely was not interpreting everything literally. It's (mostly) a real world setting, yes, but I find it's more concerned with painting an emotional picture than a logical one.