If its all a myth, what was the crisis?
The primary premise of the myth is that 'the few', that is Fighter Command or specifically 11 Group, saved Britain from an invasion in 1940. This was propagated by the media on both sides of the Atlantic not least in an effort to cultivate US public opinion for a more active role in the war prior to Pearl Harbour. You'll find this myth on the MOD/RAF site today.
According to various polls by Gallup in October 1939 only 5% of Americans were in favour of entering the war. On 6th June 1940 this was 19% 'following Italy's entrance' In July 1940 this FELL to 14% 'following the collapse of France'. In October it rose to 17% following the 'aerial blitzkrieg on Britain'. According to Gallup if the 50 million Americans who voted in the November 1940 presidential elections were asked to take a vote on whether or not to enter the war, then only 6 million would have voted 'Yes' in December. Incidentally 87% favoured taking over British possessions in the Caribbean should the Germans be victorious in 1940, the excuse being to safeguard the Panama canal !
There was a lot of work to be done in forming American public opinion.
This was done in many ways. The 'Why we Fight' series of films are obvious. Many articles appeared in the US press explaining the importance of the RN in the Atlantic to US interests. It is no coincidence that the 'Destroyers for Bases' deal was announced in September. 'Free Trade' was often mentioned. The prospect of maintaining a large standing army in 'peacetime' was raised. It may seem strange today but this was anathema to most Americans in 1940. Conscription was mentioned. Most Americans would remember the clash between Roosevelt and the Supreme Court over his effort to force a quarter of a million young men into the 'Civilian Conservation Corps' in the 1930s.
For my own reasons I have many press cuttings from the US press at this time. To say that British propaganda was uncritically reproduced would be the kindest way of summing them up

. For example on 7th September Secretary of the Navy Frank Knox, who also happened to be the publisher of the Chicago Daily News, confidently assured his readers that 'Britain has a better than even chance now of withstanding the blitzkrieg' attributing his confidence to 'Britain's superior navy.' Today we would call that 'on message'.
Another front page article trumpets.
'Pilots Have What It Takes. RAF Oblivious to Odds, Small Force Takes on 200 Nazis'. A captured German pilot is quoted, rather dubiously, in the article saying 'These Spitfires are really terrible. They're much to good for us'. I'm sure you get the picture.
11 Group was on the ropes, but so was the Luftwaffe. The RAF was not on the verge of defeat any more than the Luftwaffe was. The two air forces fought each other to a stalemate. This stalemate has been portrayed as a victory in Britain since 1940. It was in the sense that the Luftwaffe was denied its stated objectives, but it could still bomb London and other cities by night, at will.
The Germans did not even acknowledge that there had been a Battle of Britain. Their BoB was never fought, it would have taken place on English beaches or, more likely, in the middle of the Channel as they were massacred by the Home Fleet. For them the aerial campaign of July to September against mostly S.E. England was just part of a longer campaign stretching into 1941.
Unlike some (including IIRC Bungay) I do not believe that the Germans could have launched a successful invasion in the summer/autumn of 1940, even had Fighter Command been forced to withdraw north of London. I have given plenty of evidence for the Wermacht's own lack of confidence in such an operation, but here's one more, from General Gunther von Blumentritt.
'We knew far too little of England. We knew literally nothing of amphibious operations. At the time we were preparing 'Sealion' plans, accounts of the campaigns of Caesar, Britanicus and William the Conqueror were being read.'
None of this detracts from the determination and heroism of those 3,000 or so men who flew for the RAF in the battle, or the many thousands more who supported them, nor that of their adversaries. That is not part of any myth.
Cheers
Steve