Outside of PSP (which Sony could still pump out in Japan until 2014 I guess), all of Sony's hardware has had 10 year life cycles. All that means is that Sony pledges to support them for ten years by producing them and encouraging development. It doesn't mean Sony won't release a next generation PlayStation platform within ten years. They aren't going to wait until 2016 to release the next console. Heck, Sony still makes PS2s, and there are still games being released for it. PS2 came out in Japan in the year 2000.
There's also no way they drop the PlayStation branding. It may be hurting right now, but it still is quite powerful, and certainly better than starting with a new brand. The only questionable thing in regards to the name is if Sony calls it the "PlayStation 4". IIRC the number 4 has negative connotations in various Asian cultures, and is a sign of bad luck. After the PS3, and Vita Sony doesn't need more bad luck.
I would say though, don't believe these rumors unless they're actually confirmed by Sony. As Pachter pointed out, the anti-used games schlock was used against the PS3, and look what happened there. A lot of websites will use the onset of new hardware as an opportunity to spout out nonsense to get hits. They know once the real news actually comes out no one will remember their made up nonsense, and call them out on it.