I don't think that is any more likely to be true than the photo shop job of Hitler doing his little Teutonic two-step when he got news of the French surrender.
Churchill did say something to effect that the British Empire (England, Australia, New Zealand, South Africa and Canada) was "fighting by ourselves alone, but not for ourselves alone." It was truly a god send in disguise when Pearl Harbour got hit, The Americans paying a terrible price for their earlier isolationist policy.
I'm sure no one of that generation will ever forget the Lend Lease program that kept Britain in the war before the US came in, nor the tremendous industrial might that followed.
Just as in WWI, the huge influx of war material and manpower made victory possible. Thank you, America, and keep strong!