I think most of the serious Operational Analysts have looked at this and conclude that the Luftwaffe did not need to gain air superiority for an invasion. It seems far more likely that it was one of Goerings "isms" or opinions.

The Luftwaffe was very serious about sinking the British Home Seas Fleet in Scapa Flow, but did not think it could be done, as it was out of dive bomber range at it lacked an effective torpedo bomber. The Germans were not that confident about trying to sink surface platforms from level bombing. The only real option was dive bomber attack Ju-88, and that was far less accurate than Ju-87. IIRC, in 1940, the only Luftwaffe torpedo bomber was the Heinkel 115.

All in all the technical development of the Luftwaffe prior to 1939/40 indicates they did not take air power, that seriously. As the historian Ted Hooten noted, "it was like children playing marbles with diamonds!"