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Most precancels are overprints (there are the modern day exceptions)! For Bureau precancels they were applied after initial printing of the original stamp in exactly the same manner as the Shanghai, Philippines, Cuba, Guam, Kansas & Nebraska as well as other early US overprinted issues.
At least for the Kans/Nebr overprints, they were applied as part of the printing process, not after the printing. Not that that really affects your argument...