  The traditional scheme for realizing open-system quantum dynamics takes the
initial state of the system-bath composite as a simple product. Currently,
however, the issue of system-bath initial correlations possibly affecting the
reduced dynamics of the system has been attracting considerable interest. The
influential work of Shabani and Lidar [PRL {\bf 102}, 100402 (2009)] famously
related this issue to quantum discord, a concept which has in recent years
occupied the centre-stage of quantum information theory and has led to several
fundamental results. They suggested that reduced dynamics is completely
positive if and only if the initial system-bath correlations have vanishing
quantum discord. Here we show that there is, within the Shabani-Lidar
framework, no scope for any distinguished role for quantum discord in respect
of complete positivity of reduced dynamics. Since most applications of quantum
theory to real systems rests on the traditional scheme, its robustness
demonstrated here could be of far-reaching significance.
