I checked the TDP for 3rd party overclocked 7850's. They are under 120 watts. I also took a look at power consumption during gaming. The total power draw at the wall outlet for an entire desktop gaming rig with an overclocked 7850 averages around 300 watts with brief peak power draws at 400 watts.
AMD and Nvidia recommendations are conservative. By that I mean they overestimate power requirements on purpose. Let's face it, some users will purchases power supplies of really poor quality and questionable performance.