Long-term persistence of annual river runoff is a topic of ongoing hydrological research due to its implications to water resources management. In simple words, strong persistence means more intense shifts in temporal means, which might lead to clustering in the extreme values, as well as, abstract transitions between different regimes. Our estimation from 696 annual, globally distributed, streamflow records with at least 80 years, challenges the findings of previous studies, suggesting that long-term persistence might be weaker than thought. Most importantly, we show that these estimates can be reproduced by a short-term persistence stochastic model such as an auto-regressive AR(1) process. A direct consequence is that some of the most common methods for the estimation of long-term persistence, might not be suitable for discriminating short- and long-term persistence even in long observational records. Full text can be found here.