The idea of scapular stability is pushed so much that we forget about one truth: For every load-bearing joint, stability and mobility lie on a continuum. Even if there's a great need for plenty of mobility, there's still a mild need for some stability, and vice versa.
In the case of the scapulae, stability is king, but the body must posses the capacity to move the scapulae around at will. This will contribute to healthy, pain-free shoulders, and also allow the shoulder joint to move freely. People with good scapular mobility won't have problems performing prone plate transfers.
In the video, I'm only using a 2.5 pound plate. With my clients, I use their water bottle or one of my fat grips. The point is, it's very easy to let technique go out the window, and it's extremely humbling, even with the lightest of loads. Keeping everything possible off the mat is harder than it looks.