Kohler's installation instructions say for the tub to sit on only its 4 machined feet.
*However*, these feet are very skinny (<1/4" wide) and will sink into the floor unless placed on metal shims. Also, they are not necessarily in-plane with each other. The Kohler Villager I just installed had warped and its feet were 1/8" out-of-plane. Wobbly tub, leaky drain (eventually).
I eventually used a ledger board (despite Kohler's instructions saying not to) and am glad I did. No wobble. No sinking into the floor. Rock solid.