We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a serious pitfall generally causing difficulties in the effective modeling of the controlled system. We show that at present, to avoid these problems, a full microscopic description of the controlled system in the presence of noise may often be necessary. We illustrate our findings with a paradigmatic example.