I was told that if you buy the higher octane gas which is better for your vehicle, but is obviously more expensive would in the end cost the same. Do to the fact that the higher octane makes your car drive more efficiently. Is this fact or fiction?

Fiction. Although filling up with a bit of the slightly higher-octane stuff once in a great while can supposedly clean the engine a bit and increase its longevity, there is no benefit to regularly filling up with a higher octane than your engine is optimized for - IE, the manufacturer recommended level. If you go higher, it will more than likely DECREASE your fuel economy because your engine isn't designed for it.

Contrary to popular belief, most ECUs canNOT automatically correct for a change in octane level. Most modern ones can be reprogrammed to adjust for it, but that's only part of the equation for making an engine run efficiently on a certain octane.

If you're lucky, your fuel economy would stay about the same. In the long run, going to a higher octane will almost always cost you more in the long run. The only time it won't is if you modify the engine specifically for it, and if you make any errors in the adjustment you will decrease the longevity of your engine. Not a risk worth taking unless we suddenly have a complete and total switch to Ethanol and we MUST mod our engines for it. Obviously, that's not gonna happen.

Higher Octane fuels burn slower and thus produce less energy for a given volume of fuel. In this regard higher octane fuel will generally reduce your fuel economy.

Higher octane fuel, because it burns slower, is also more stable. This increased stability afford it the ability to handle higher compression and more timing advance.

Both of those (to a degree) are better for performance.

If your vehicle doesn't need the octane, it's not going to perform any better with it, nor will it get better economy.