As a thought experiment, let's consider a pulse that has been band-limited to 20kHz. Are you arguing that the analog output of a (filtered, idealized) DAC would look different depending on whether the dac was running at 44.1kHz vs 192kHz? If so, I don't think many people would agree with you.
Any difference in the "timing" of the output wave would have to come from energy that falls above nyquist of the slower sample rate. So, while I agree with you that the timing would be sharper, this is exactly caused by "higher frequencies", not by some other sort of timing improvement.