It will definitely run on 300W, this guy has no idea what he's talking about.
There are pre-configured HP Pc's with HD 7750's and 300W that run perfectly fine, so you'll be okay.
Manufacturers put up higher wattages than needed because many cheap, aftermarket power supplies cannot output the wattage that they are rated for, so they put higher wattages on the website to prevent complaints. For example, Tom's has done reviews on $20 power supplies rated 500W and blow up before reaching 200W, literally they spark, smoke, and die.
Well actually I speak from experience which you probably know nothing about since your all about reviews. I've had video cards on low end PC's that need a minimum of 300 and I even had a 300w. And the system was completely slowed. Took about 5-10 mins to boot into windows. To come here and tell people they don't know what there talking about is rude, disrespectful, and self centered. Were all of these forums to get help, and help others. Your right I could be completely wrong. But even if you were wrong and I was right (which I am because its happened to me about 5 times) I still wouldn't tell you that you have no idea what your talking about. Please take your ignorance somewhere else.