Prof. Lewin is right. KVL is a conditional law based on conditions that no time changing mag fields are present. It holds when this condition is met. KVL is not a universal law. When a mag field changes w/ time, the sum of voltages around a loop is non-zero.
So 2 elements in parallel are not at the same voltage. The voltage from a to b depends upon the path taken. Dr. Lewin does a good job explaining this. I had to work with these principles for years when I was in magnetic component development. When designing inductors, transformers, rf chokes, motor drives, regenerative braking, etc., I became accustomed to knowing that KVL only holds when no time changing mag fields are present. It became second nature.
Those whose experience w/ electronics does not include magnetics will at first struggle with Dr. Lewin's teachings. It seems counter-intuituve at first glance. But Maxwell & others have verified their claims & over a century of scientific testing/observation have afformed the same.
Dr. Lewin is on solid ground, for sure.