Head postion in Freestyle single stroke unilateral swimming

I have been through all the “head postion” threads in this forums but could not trace anything to a confusion I would like to clear. If a person is breathing every stroke from the same side in freestyle, when after taking a breath, the body (hips and shoulders) twists to the other side(under the water as this is not bilateral swimming), would not the head also tilt towards the other side with the hips and shoulders or is one supposed to keep the head straight down. For instance, If I am breathing on the right at every stroke, when I tilt towards the left underwater after taking a breath, would not the head(under the water) also tilt towards the left with hips and shoulders to maintain the streamline position or is it that when I twist my hips and shoulders towards the left, the head should stare down which is normally recommended(assuming that I will take a breath again on the right)?From what I know the head and shoulders have to rotate symmetrically both ways to reduce drag. Should it not be likewise for the head for this kind of swimming(Unilateral swimming I presume- bilateral does not suit me currently).