Time to understand where the recommended power supply requirements come from.
AMD and nVidia have a test system that they use, it tends to be a pretty hefty system that they plug the GPU into and figure out total system power consumption from, well since the system itself is pretty hefty it really couldnt run on much less than 400W even without a graphics card, hence the 400W recomendation.
Now, to understand how much power you actually need it really depends on the system, if you were going to put the 6450 in a system with an OC'ed 2600K, a half dozen hard drives and fans then you would need close to 400W, but most people are putting the 6450 in a small lower powered system with a 65W CPU, one maybe 2 hard drives, and nothing else that needs significant amounts of power so you can get by with a 250W unit IF you know the hardware in the system and never plan on upgrades.
HP and the like always put the smallest PSU they can in a system to save on money, but it also restricts upgraded potential significantly but that isnt their concern. So while your 250W is fine for a 6450, it might not be for some of the bigger cards that still recommend 400W power supplies.