I have come across some papers in biochemistry that seem to claim that a reaction can be "near equilibrium" even though the flux through the reaction (net reaction rate) is large. For example, this paper measures absolute metabolite concentrations in E.Coli cells grown on two carbon sources, performs some thermodynamic calculations, and concludes that "lower glycolysis is near equilibrium on both carbon sources, with $\Delta G$ approximately 0". Yet this pathway carries net flux in these conditions according to the authors, and usually glycolytic flux is rather large.
How can this be? In my understanding, the net rate of a reaction depends on the Gibbs energy $\Delta G$ so that, near equilibrium where $\Delta G \approx 0$, there is no net flux through the reaction. And I think this dependence should be smooth, so that $\Delta G$ must be large when the net rate is large?
The authors suggest that reaction rate depends steeply on $\Delta G$, so that "Small changes in $Q$ are accordingly adequate to tip the thermodynamically favored flux direction." (From the supplementary it looks like the reaction quotient $Q$ varies between 0.5 and 6.) I have also encountered this idea in works on thermodynamic flux analysis, where only the sign of $\Delta G$ is considered important, its magnitude $|\Delta G|$ is ignored. But if this is true, the reaction direction seems unpredictable and the system should be difficult to control?
Is this all just a question of what "small" or "large" $\Delta G$ means? Can the dependence on $\Delta G$ be sharp, so that the sign of $\Delta G$ acts like a "switch"? Can a reaction really be considered "near equilibrium" if the net reaction rate is large?