Social media can be used for disaster risk reduction as a complement to traditional information sources, and the literature has suggested numerous ways to achieve this. In the case of floods, for instance, data collection from social media can be triggered by a severe weather forecast and/or a flood prediction. By way of contrast, in this paper we explore the possibility of having an entirely independent flood monitoring system which is based completely on social media, and which is completely self-activated. This independence and self-activation would bring increased robustness, as the system would not depend on other mechanisms for forecasting. We observe that social media can indeed help in the early detection of some flood events that would otherwise not be detected until later, albeit at the cost of many false positives. Overall, our experiments suggest that social media signals should only be used to complement existing monitoring systems, and we provide various explanations to support this argument.