Nowadays, due to excessive queuing, delays on the Internet can grow longer than several round trips between the Moon and the Earth, for which the "bufferbloat" term was recently coined. Some point to active queue management (AQM) as the solution. Others propose end-to-end low-priority congestion control techniques (LPCC). Under both approaches, promising advances have been made in recent times: notable examples are CoDel for AQM, and LEDBAT for LPCC. In this paper, we warn of a potentially fateful interaction when AQM and LPCC techniques are combined: namely (i) AQM resets the relative level of priority between best effort and low-priority congestion control protocols; (ii) while reprioritization generally equalizes the priority of LPCC and TCP, we also find that some AQM settings may actually lead best effort TCP to starvation. By an extended set of experiments conducted on both controlled testbeds and on the Internet, we show the problem to hold in the real world for all tested combination of AQM policies and LPCC protocols. To further validate the generality of our findings, we complement our experiments with packet-level simulation, to cover cases of other popular AQM and LPCC that are not available in the Linux kernel. To promote cross-comparison, we make our scripts and dataset available to the research community.