Are we talking about the same system? PS2 all but died within a year after PS3 launched, aside from a bit of shovelware here and there and the very occasional half decent title (and even then, most of those were simply ports made for the Wii). And that was WITH the BC that PS3 had with PS2, and the fact that the PS2 was the best selling system ever. Just because they kept pumping out systems and "Greatest Hits" games doesn't mean that the system was truely alive. So, by your logic, the Wii is still alive and well just because the console is still being produced, even though it hasn't recieved a noteworthy title in months (Pandora's Tower), or for most gamers years (Skyward Sword).
No, I see no chance of PS3 getting any real support after 2014 unless, like PS2, it's getting ports of WiiU versions of games, but given how poorly those sold I doubt WiiU/PS3 will even get that. Sony can say whatever they want, and I've no doubt the fanboys will eat it up, but there is a huge difference between reality and PR statements.