Depth of the stances was an usual way to differentiate southern and northern chinese martial arts (nanquan vs chanquan) styles. Southern ones use to do very deep stances, and northern more natural or high, supposedly because kind of terrains from one part of china to another. Since history says that southern chinese styles are one of the major roots of okinawan kempo, the deep squatting position (kiba dachi) that one can say in many katas, but specially in naihanchi or tekki, would depend from this source. However, Choki Motobu (who supposedly was the inspiration for Mitose's adoption of naihanchi) in his book Watashi no karate jutsu, shows an interpretation of Naihanchi that uses a square kiba dachi not that deep as Funakoshi's one, important point since they both trained in some moment of their careers under Anko Itosu, who's credited as the one that made the three naihanchi katas by breaking an older chinese form. So in this case, i think is not about the teacher they had but the way they both understand the relationship of kata training with real fighting. Since Funakoshi approach to movement is heavily influenced by kendo idea of ending the confrontation with just one strike, they tend to understand the stances thinking in to get the most stability, reach and power that is possible by deepen the body center of gravity. In Motobu's approach stances also work as source of power but as stages of a flow (like in modern kenpo) that could support many strikes and changes in the fighting situation.
