I can see that on a flat surface the tension in the calf as the knee bends would tend to make the quads do less work.
A further couple of points on squats:
1/ do not let the knee(s) bend in towards each other - you should be able to just see the side of your big toe as you look down the inner side of your knee
2/ it is the initial taking up of tension that particularly strengthens tendons, so if going lower is difficult/painful, even those first few degrees of bend are beneficial.