In this paper, we compare and evaluate different testing protocols used for automatic COVID-19 diagnosis from X-Ray images in the recent literature. We show that similar results can be obtained using X-Ray images that do not contain most of the lungs. We are able to remove the lungs from the images by turning to black the center of the X-Ray scan and training our classifiers only on the outer part of the images. Hence, we deduce that several testing protocols for the recognition are not fair and that the neural networks are learning patterns in the dataset that are not correlated to the presence of COVID-19. Finally, we show that creating a fair testing protocol is a challenging task, and we provide a method to measure how fair a specific testing protocol is. In the future research we suggest to check the fairness of a testing protocol using our tools and we encourage researchers to look for better techniques than the ones that we propose.