Long after I'd left the cinema (and forgotten most of the detail of Total Recall - oh the irony!) I remember that line in the trailer and it got me thinking about it's usage to sell a obviously fictional story. 'Based on a true story' gives a movie, or book, or whatever, a grounding in reality; something tangible to the viewing audience. I suppose it can make it more engaging, perhaps fire the imagination, and make the drama more 'real' since it might have happened, and it can draw in the audience.
Basically exactly what a GM is trying to do at the gaming table.
Anyone that has GMed for any length of time is sure to have seen advice on basing stories on real life - stealing plots from the all over the place, but I wonder how many people make a point of telling the players this? Admittedly this is unlikely to have the right impact in your typical D&D Fantasy game, but if you're playing a game like Call of Cthulhu, Delta Green, or similar, then I reckon there might be significant impact to be had through silently, and without explanation, holding up a sign at the beginning of your first introductory narrative, that simply says 'Based on a True Story'.
Of course, for your own credibility (because you know the players will ask later) it's kind of important that the adventure is 'based' on a true story - or perhaps 'inspired' by it at least! But there are enough mysteries for you to easily pluck a story from the popular media and use that as the basis of your story. Adding tentacles, sea monsters, or aliens later doesn't stop your story being 'based' on a true story does it?
Yes it's a bit of a party trick, but so it a lot of effective story telling and if it engages your players then there's no apology necessary. Just don't do it all the time as it does become a cliche..
In case you're interested The Possession is apparently based on the story of The Dibbuk Box. I'll leave it to you to decide whether that is a good thing..