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Build a still at home to test your theory, and distill the different grades. If more octane comes out of the higher-octane grade, the myth will be busted.
No great loss.
Building a still at home presents problems not the least of which may be legality. Ethanol (still product) readily absorbs water so it would need to be dehydrated before using in a gasoline engine else you may get too much water in your gas tank (not good). Also getting octanes out of your homemade still is nigh on impossible. Octanes are a family of hydrocarbons that are typical components of gasoline manufacture which is a complex operation. They are colorless liquids that boil around 125 °C (260 °F). Homemade stills rarely exceed 195° F in ethanol manufacture.