You sound as though you are anatomically educated. Or you are very crafty with Google. Either way…not an anotomical reference but Badha Konasana is typically refered to as a groin opener. The muscles that externally rotate the femur are pullers like the piriformis. It doesn’t make much sense to me to lay the responsibility on the piriformis since it’s doing it’s job. But it’s receiveing resistance.
The Sartorius is a hip flexor. As such it’s responsible for lifting the femur up toward the torso. Is there hip flexion in Badha Konasana (though this might be more of a statement of degrees rather than an all or none)?
I’m not sure of the preoccupation with knees to the floor as it’s quite irrelevant. The knees should be kept safe and the floor isn’t always the safest place for them relative to the anatomy of the practitioner.
But that’s not your question, now is it?
Since medial rotation is achieved using the TFL and the Gluteus Medius (as well as anterior fibers of the Gluteus Minimus) I would think these folks are the tight ones holding the external rotation back in Badha Kionasana. But I’m just surmising.