To make the case that I "claimed -- falsely -- that these 'allegations' are 'unmitigated and unsupported nonsense.'", you have to support them as supported fact, mitigated or otherwise.

Otherwise you can write "the cause of miracles is leprechauns" or "Venusians live next door" and than take the position you're currently taking that it is up to others to disprove that unmitigated and unsupported nonsense.

A quick Google of "natural law" with, sequentially, trains, airplanes, and anesthesia turns up zero references supporting Mr. Shea.