Speaking as an engineer (electronic, not flight), it appears that there's a fundamental design fault in how ILS works if it can lose the modulation and still convince an approaching aircraft that it's happily on the correct slope. You almost want to deliberately wobble up and down slightly on approach if it claims a perfect and instant capture just to prove it will tell you to get back on the appropriate slope. I've evolved a very "what if?" approach to things over the years to try and pick up obscure failure modes, and aviation is a rich source of things the designers didn't think of, partly because it's so public and well-documented after the event.
For those that didn't spot it, one of the contributors to the YouTube thread posted a longer version of the video that includes a simplified version of how ILS works and what was wrong in this case.