Final answer:
The iliacus and psoas major muscles do not externally rotate the hip but are responsible for hip flexion. The lateral rotators such as the piriformis and obturator muscles facilitate external rotation of the hip.
Step-by-step explanation:
The iliacus and psoas major do not externally rotate the hip; they are primarily responsible for hip flexion. The reason provided for external rotation in the question is incorrect; these muscles have a slightly more anterior insertion on the lesser trochanter relative to their more anterior origins, which aids in hip flexion.
The lateral rotators of the thigh at the hip, which include the piriformis, obturator internus, obturator externus, superior gemellus, inferior gemellus, and quadratus femoris, are responsible for externally rotating the femur at the hip.