It stands to reason that under the imperius curse, Barty Crouch would draft letters in his own handwriting in there for Percy Weasley was correct in identifying the authenticity of the owls that sent him instructions. He still faced an inquiry at work for having not been able to realize that the letters were not authentic. However, in that same book, Mad-Eye Moody points out that it's almost impossible to recognize when someone is under the imperius curse because they are made to do the bidding of the witch or wizard who cursed them which, in this case would legitimately mean sending owls.