Also, apparently, the rocket exhaust actually recirculated up the sides of the Saturn V inside the boundary layer, well past the point where the fins attached. See the picture in the following paper, where it appears that the exhaust is originating from a point about halfway up the first stage.

https://www.nas.nasa.gov/assets/pdf/Kiris_Gusman_PlumeCFD.pd...

Which tells you something about the size of the Saturn V boundary layer.