the moon has 5 different months, none of them are 28 days.
The progression of lunar cycles is 29.53059 days. That is the time from one new moon to another.
the other 4 months are around 27.5 days, and have to do with the moons orbit around the earth.
moon cycles are caused by the fact that the moon wobbles in its orbit. the moon is literally closer to the earth during the full moon, and occupies more space in the sky.
Old time wisdom has to do with the moon's progression through certain constellations and across certain stars, and its phases during those times. I suspect that this has more to do with establishing a point of reference to measure from than thinking that the stars hold sway over the earth.
The moon wobbles in its orbit, and at the same time it rotates around the earth. The cycle of its wobble, it's orbit, and its day are more or less the same, which means that the same side of the moon is always facing the earth.