Not necessarily. This is the full hip rotation stroke which I think is about 30-45 deg rotation.
Also, its not necessarily a left to right weight transfer - if the ball is to your right hip or more you actually load up your right leg and push off it (while rotating hips). If ball is to your left side you load up your left leg. You actually push off both legs if it's to your middle. The reason why it's unintuitive is because, the hip rotation is more of an internal hip rotation where you rotate inwards, not externally like the FH.
Against fast topspin, you don't rotate 30-45 deg, maybe only 5-15 deg but the rotation has to be there if you want to get any kind of good power and control over the shot. If you make a stroke smaller, it should have all the same components except in a smaller magnitude, otherwise when do you know when to use full stroke vs abbreviated stroke? Having gears in your movement ensures that you have a smooth transition to all balls.
Also, hip rotation is way faster than moving your arms. This also applies to FH. Even straightening arm during backswing is a waste of precious backswing time, when you can just rotate hips to backswing, forward swing and then recover (also with the hips).
No, that's the wrong way of teaching it, and it's part of the reason I along apparently some others think online tutorials are useless.
The close to the table shot is not merely a smaller variation of the away from the table or vs backspin shot.
The key here is that the ratio of waist rotation vs spinal flexion/extension is different between the two shots. The larger motion loop is more like an analog of the FH shot, with a very pronounced left/right rotation, good whip motion from the legs to the waist to all the joints of the upper extremity sequentially. The mistake is to teach the close to the table shot similarly, thinking it's just the same mechanics but with a smaller motion. It doesn't look the same, as others have pointed out, yet all sorts of teachers think they're the same and teach them the same way. That's wrong.
You touched on the difference between the two, albeit using incorrect terms. You said it's more like an "internal rotation". Internal and exertnal rotation refer to the limbs as it rotates around the trunk, while the trunk, as the point of reference, does not internally or externally rotate. I get what you mean though, the rotation is not predominantly right to left. You're flexing your hip and your spine at both the lumbar and thoracic regions during the backswing. The lumbar/hip flexion kicks your hip out, the thoracic flexion brings your shoulder down, and the right to left rotation adds a diagonal component. The resulting overall motion is what you actually see, the the left hip kicks out to the left (and thus belly sucked in while the left leg flexes), and the shoulder is brought down and to the left.
That's the primary motion for a close to the table shot. The larger motion shot involves a much larger component of the left/right rotation, while the smaller motion is primarily flexion of the spine/hip, with a bit of rotation.
When I was trying to add body to my BH shot, I initially tried the left/right rotation method, but it was a disaster with quicker counters. I gave up on it, and instead focused on adjusting my body to ensure the ball comes to my strike zone. When the ball came fast, I naturally lowered my body and kicked my hip out to the left to give me a bit of additional space to get to the ball. Then when I struck the ball with all my power, my body naturally tensed up and returned to the neutral position. It ended up looking exactly like how the pros showed it, and I wasn't even trying to make it happen.
IMO that's the correct way to approach body usage in close counters. If you try to approach it from the left/right rotation method, you'll never get there. This is especially true if you start off your BH practice with power loops of backspins or away from the table. That's a very natural motion, you get used to that and try to just use a smaller version of the same motion you'll end up with the wrong ratio of rotation vs spinal flex/extension.