What was the answer you found?
We're working around this problem by disabling one or both of the "Multimedia plugins" and "Convert URLs into links and images" filters at the module or course level. If both filters are enabled, Moodle breaks embed code copied directly from YouTube, but http "Share this video" links still work.
This problem seemed to be introduced during our upgrade from 2.3.6 to 2.3.8.