Shoulder lead indeed sounds strange ... but if you dance OP or PP step, hips are not turned towards the partner as much as shoulder area,
For promenade I would agree. Ideally the partners’ shoulders are still perfectly parallel in promenade, also parallel to the line of advance. However the leader’s right foot - follower’s left - could not step through if the hips were also parallel, so the hips need to angle away from each other slightly; angling 45 degrees from the shoulder line, creating a 90 degree V, works well, allowing the inside legs and feet to step between the outside Legs and feet without creating too wide a look. With parallel shoulders in the hold, the offset to partner’s right keeps the lady’s hip behind the man’s hip, incidentally facilitating stepping through with the inside legs by allowing the lady’s leg to follow the man’s leg through, so that space is required for only one leg at a time.
For outside partner I disagree. In a square dance frame, maximum separation between the partners is not perpendicular to their shoulders; rather, because of the partnership offset, it is along an axis at a diagonal to the shoulders. To maximize the space available for the outside partner step, this axis should be at right angles to the line of advance, meaning that the shoulders should be at an angle to the line of advance, not parallel. The ideal angle may differ somewhat from couple to couple depending on the depth of the dancers’ rib cages, but is in the range of 45 degrees for most couples.
The perfect angling of the hips may also differ from couple to couple, but in no case does the thigh of the leg stepping outside partner need to fully pass through the partnership gap, as its hip joint remains behind the other hip of the forward moving partner because of the angling of the hips toward partner. Typically the thickest part of the leg that needs to pass outside partner is closer to the knee than the hip, and this is at a point where the leg is considerably thinner than it’s thickest point.
otherwise step ends up way too short.
Any reduction in step length because of angling the body towards partner when outside partner should be fully compensated for by the increase in the length of the preceding step from the same angle.
If one is still worried about the length of the step outside partner - which most coaches teach as a small step - one can focus one’s efforts concerning step elongation on better articulation of the ankles and feet and on maximizing the swing angle at the knee, rather than at the hip.
Core is twisted between shoulder area and hips. So it's indeed more accurate description than side lead.
Since the ideal shoulder or rib cage angle is in principle different from the ideal hip angle, there may be couples where a larger shoulder angle is ideal. However, there may also be couples where the ideal is to angle the hips toward partner more than the shoulders. Angling them the same amount should be fine for syllabus dancers, and in my opinion the hip angle is more important for getting the “feel” of outside partner, and for leading it properly.