The problem is, that Israel made it relatively easy to fall for these stories by doing similar things for real in the past.
So you’ve got a credible source (BBC) reporting something that’s not really unheard of (i.e. kind of plausible) and that’s happening to align with what you’ve already suspected. Bam, rumor is born.
BTW, you had the same mechanism shortly after the attacks with the “Hamas beheaded babies” stories.