The point is they never LOST their nationality, that was idle threat that was quickly swept under the rug....
And no one ever said the Eagle Squadron fought in the B of B.
"As I walked across the bridge that morning I stopped and looked down at the swirling waters, wondering where they might carry me. I was leaving a country at peace, still becalmed in the depression, and going to one at war, fighting for it survival. I was more excited than frightened. Most of my family and friends were baffled. My own government was still in the sway of those who wanted to turn a blind eye to Hilter. It was not our war. It was not my fight. I had heard it all, but I kept on walking.
For a moment when I re-entered the RCAF recruiting station, my thoughts became mundane. Would they throw me out again, for being too thin, or too fat, as if I was in some mad version of Goldilocks and the three bears ? This time however, when I stepped onto the airforce weighing scales like a prize-fighter, the entire office cheered, I was in.
But there was price to pay. Like every American who joined up in Canada, years before America entered the war, I immediately had my citizenship and passport revoked for the crime of fighting for the King. The fact that so many of us Americans who volunteered in the Second World War before the United States entered it lost our citizenship for the privelage of being shot at in the interests of freedom remains to this day one of the least reported and least glorious chapters in the history of our early neutrality in the conflict. The US governments attitiude was simple : to fight for Britain you have to swear allegiance to the King and to do that you lose your American citizenship. I thought about it for a moment, my pen poised above the enlistment papers that would chamge my life. Then I went ahead and signed up. There are some things more important than bits of paper."
William Ash.
"Under the Wire"
Read his book...
[Sorry my mistake not a BoB pilot as he signed up in early 1940... but he is a Spitfire pilot and a remarkable man]