First, the provocation test for femoral acetabular impingment is combined flexion, adduction, and internal rotation – essentially a knee-caved squat postion. This is a provocation test because it replicates an impingement and pinches the irritated tissue together. Producing this movement under load is a good way to injure yourself, but that’s not really what you’re asking about.
So what happens if you can’t internally rotate through a full functional range? Well, when you consider that the role of adductors and abductors during squats, gait, [insert closed chain exercise here] is to stabilize the hip, with limited internal rotation these guys aren’t producing balanced forces across the hip joint (either because they don’t need to or they can’t). Then you end up predisposed to hip OA (pain on squatting is another sign of this). This is bad.
Now, how does this influence one’s ability to hit depth in a squat safely, like your article talks about? It comes back to the arthrokinematics of the hip joint in a squat. If internal rotation is limited, the external rotators are dominating, which drives the head of the femur anteriorly in the acetabulum. In order to get deep hip flexion, the front side of the head of the femur has to have some room to rotate up in the sagittal plane. With the limited internal rotation pushing it forward into the joint capsule, the femur isn’t free to rotate up like it should, and you end up with a lot of uneven stress on the joint capsule and labrum. This’ll usually lock up your hip before you hit full hip flexion, leading to lumbar rounding, hip pain, or both. This is also bad.
The last point comes down to motor control. If the body doesn’t know that a range is available to it, it’s not going to work in that range. You don’t want internal rotation to happen in a squat in the sense that you don’t want your knees caving in and causing impingement at the hip and valgus stresses at the knee. However, you want the motionavailable so that the adductors, abductors, and internal/external rotators fire in the appropriate pattern to distribute the forces in the hip as broadly as possible. Without having the available range, that muscle action will be inhibited and you’ll end up with uneven loads, pain, and a problem that perpetuates itself until you’re too messed up to do anything about it.