You can get up to 1" (yes one inch!!) of tire carcass deformation, even with a 35-series sidewall on a properly sized rim. You've seen the undercar videos of AI cars (Toyo RR) digging into a corner, and seen the entire carcass shift towards the inside of the car (outside front wheel), more at the bottom than at the top, but the entire carcass is moving back and forth relative to the wheel centerline.
What you're missing is the axle pivoting around the roll center of the rear suspension. Rear roll center with a Panhard is essentially defined as the point where the track bar crosses the center of the differential housing. This will move vertically, slightly, depending on whether it's a left or right turn, but honestly not all that much with properly selected spring rates. With a Watts, the RC is essentially defined as the center of the pivot bolt. That will move relative the axle, or not, depending on whether the pivot is fixed to the rear cover (Griggs) or is mounted to the sprung chassis (Fays2). With the camera on the car fixed to the chassis, visually, the axle is moving around the roll center. When it does, the position of the wheel relative to the wheel well NECESSARILY has to change, regardless of locating mechanism.
View attachment 57278
Black line is the chassis plane, static relative to the camera in the video. Green is the axle and tires with no side load. The dot in the middle is the roll-center. Red is the axle under pure roll conditions, with no pitch (throttle or braking induced load transfer).
As you can pretty clearly see, the tire "appears" to move in and out of the wheelwell (relative to the black chassis plane), when in reality it really doesn't. It's just a function of the visual angle. This is somewhat compounded by the carcass deformation, where the outside tire, the left in this case, will have the contact patch shoved violently inward (the aforementioned 1"), with the outside tire being shoved slightly the other way (light load, small carcass centerline shift). In terms of the video, those two "stack up" (thanks Kelly!!) and you have what appears to be an axle shifting back and forth dramatically. If this were actually the case, where the entire housing was moving laterally relative to the chassis by
inches, you would see it not only at the wheel, like in the famous video, but also TO THE SAME EXTENT right at the roll center. In the undercar video though, if you focus on the center of the diff, it isn't moving much relative to the rest of the chassis, which means that the axle itself isn't moving much. Looking at the roll center will show you how much lateral migration there really isn't. If you catch my drift.
Does the Watts control the lateral position of the axle better than a Panhard bar? Yes. That's not up for debate, at all. Is it 0.1%, 1%, 10%, 100%, 1000% better? THAT is what is up for debate, particularly when you're talking about a street-driven car, when NOT driving like you're an ass-hat. Think in terms of taking a corner with a MOST a 0.20G lateral load, not a 1.0G autocross turn...
Trivia quiz: Name the SPEC SERIES, professional level, that allows the use of either a Panhard bar or a Watts link. Hints: V8s, tube chassis, quick-change rear end. Both Watts and PHB are available, and to the best of my knowledge legal. If it was such a night-and-day difference, wouldn't that be as closely regulated as everything else on the car, as is typical of a spec series?