Hello, this is ganador01, your resident myth buster. Yes, many of us have heard this claim over the years. It is true to an extent. If you have an older car that has a quite a few miles on it (50,000+ in desperate need of a fluids change), changing to synthetic fluids all around could net u a gain in HP. This being becuase the old fluids have "gunked" up the system. What synthetics do is put ur car back in great running condition. They are better formulated and generally are a tiny bit better on the lubrication/heat withstanding side. But, I highly doubt you will get any HP gain over factory fluid on a brand new car.
Speaking on the lines of motor oil, almost all new cars are built in a way to maximize the performance from the factory. If ford could justify synthetic fluid from the factory, every one of their cars would carry it. The thing is, brand new, synthetic oil = dinosaur oil.
Also take note that synthetic oil can bring up leaks in ur system. It is generally a thinner oil in nature and will not clump like "dinosaur oil". Not only will it not clump, it will also unclump previous clogs that may be in ur system. Hence, if you had a cracked line that was filled with old dried up motor oil, it would be renewed and begin leaking again by running synthetic through it.