Direct numerical simulation data obtained from a statistically stationary, 1D, planar, weakly turbulent, premixed flame, which is associated with the flamelet combustion regime, are analyzed in order to show that generation of vorticity due to baroclinic torque within flamelets can impede wrinkling the reaction surface, reduce its area, and decrease the burning rate. These data call for revisiting the widely accepted concept of combustion acceleration due to flame-generated turbulence.