We see that reality play out on the ground in rhetoric all the time. Anti-trans activists like representatives from the UK’s LGB Alliance routinely make false claims about trans criminality, often resorting to anecdote because data don’t back them up.
It’s telling that those anecdotes are scarce to the point of being impossible to find. In fact, the one case they often end up citing is so bizarre it raises eyebrows when people learn the details.
The truth is the trans women do not represent a threat, and the only way to create a threat in people’s minds is to distort reality.