LoRaWAN is a major player for IoT data collection in large areas. In such networks, the uplink is mainly used, especially for data transmission, whereas the downlink is used for control purposes, including physical layer configuration, over the air activation and acknowledgments. In most studies of the LoRaWAN capacity, the uplink and the downlink are supposed to be orthogonal. This assumption seems acceptable and correct because the LoRa physical layer uses an inverse modulation for the uplink and the downlink. In this work, we use a real testbed composed of software-defined radio (USRPs, GNU Radio) to show that this assumption is wrong: the frame delivery rate decreases by up to 20% when simultaneous transmissions occur between the uplink and the downlink. As far as we know, it is the first time that this result is shown.