Thanks to Forum user YouJustLostThe Game for bringing this to our attention. Turns out that early access to the Heavy Rain demo can be granted to just about anyone!
Head to http://www.precinct52.com/case1117_briefing and register for the site, when your done log in and continue to the evidence room.
Here select the four pieces of evidence,
Coffee Shop C (says Diner in the Picture)
Select Cigerette butts, and choose the smaller one
Select Tyre prints and choose 117/H
When your done submit the evidence and collect your code to download the Demo 1 week early! The demo itself features 2 scenes from Chapter 2 of the game.
Post your thoughts in the comments!