I find this argument really weak, and the patronising tone unhelpful. A degree of faux naivete, perhaps. If not...
On the reporting front.
They're failing.
Our national broadcaster has a mandate to provide clear, accurate information to the public, and this was neither clear nor accurate.
If the source is untrustworthy or misleading, as (to my endless astonishment) in this case, this must be acknowledged or followed up, not simply "reported" as fact.
If the terminology is unclear, as the word "woman" now is, this should be contextualised or clarified.
Approaches necessary to upholding their mandate in this difficult context could range from surveying the public's understanding of rapidly shifting language (recent, smaller-scale surveys have suggested a significant proportion are not aware that "woman" may mean "transwoman", nor even that "transwoman" is a male identifying as female, as opposed to the other way around), to using quotation marks or more careful phrasing that makes it clear that the language used and judgement made regarding this individual's sex/gender is that of the police, and not necessarily the BBC.
On the journalism front.
They're failing.
They're aware of the ongoing debate regarding the meaning of the word "woman" and the controversial adoption of different interpretations of this in different contexts, yet have unambiguously aligned themselves with one side - to the extent that they elect to use both "woman" and "female" for male criminals when other less influential publications ascertain and report the culprit as a "transwoman", and challenged one of their own journalists for seeking to clarify the latter term in his reporting. This readiness to unquestioningly replicate other public institutions' adoption of highly politicised language at the expense of public understanding sets an exceptionally dangerous precedent for our democracy.
Woman and girls are being denied the relevant knowledge to make the necessary judgements about their safety. Some remain unaware that single sex spaces are no longer protected by the social contract on which we all used to rely - that blissfully reassuring confidence that someone else witnessing a man follow you into a loo would have every reason to assume malicious intent and would call him out on it. Meanwhile, those of us in-the-know from reading other publications' more thorough and precise reporting are struggling to ascertain the truth of claims that transwomen present less of a threat to us.
Actually, prison statistics indicate that they do, quite clearly, present the same threat, if not a considerably higher one. So where's the investigative journalism on this huge issue? Where are the "fact-checkers" and "explainers" deemed important in other contexts? Where' the evidence that the BBC is fulfilling its journalistic responsibilities here?*
*See also the WPATH files.