Fighting against an obvious hoax is not the same as falling hook, line and sinker for it. One fights because so many others have fallen for the hoax and thus their behavior supports it. Belief in the hoax produces real world consequences that affect us all.
Example: We fight against the Manmade Global Warming hoax because so many who have fallen for it are supporting government policies that harm us all. Simply pointing out the obvious scientific flaws and failures of the theory and leaving it at that is de facto surrender on the policy front. One must relentlessly employ the real science that exposes the hoax for what it is, and hope that eventually support for it erodes, one mind at a time.
Heying fights back. Good for her.