While some of the individual scenes had inevitable conclusions regardless of what you did, there were a ton of different endings in that game and consequences for what you did. In the backward driving scene if you fail, you don't get the clue. There are other ways around missing clues but it was still a consequence.
The overall ending of the game differed wildly based on all those things. I do see what you are saying - you are kind of on rails for some of the individual sequences in Heavy Rain - but everything does eventually add up. Not necessarily in a coherent way. :-)
The only point I was making with Heavy Rain vs Mass Effect is that both I believe are guilty of some serious narrative problems, but for some reason Heavy Rain tends to get crushed for its narrative more often than Mass Effect. The salient point has been made that Heavy Rain relies more... uh... heavily on its narrative as the reason to play than Mass Effect, and that's a fair point, but it doesn't change the existence of plot holes and narrative wackiness in both stories. Mass Effect does have more replayability IMO since it has more compelling gameplay overall, but I'm just talking about narrative by itself here - Mass Effect always seems to get a pass for some reason for the same type of narrative mistakes that other games get crushed for.