I am intrigued by this case.
The lady in question joined the full-time police service after her gender reassignment, and through her previous role, she would be aware - as is anyone with even a passing intrerest in the way the police work - that using a radio is going to be a daily and vital aspect of her duties. From my (limited) knowledge, assignment does not change the pitch of the voice of the reassignee who is going to have to live with a 'male' voice, even if everything else is female.
So the notion that she did not expect to be challeneged at least once about the sound of her voice is a total nonsense - she could, as advised, have simply have said that she had a deep voice.
I work for BT, and years ago, worked with a lovely lady who had a really deep voice, and was constnatly mistaken for a man on the phone, which she always laughed about, and accepted.
This lady worked for the Malicious Calls Section, and was passed a case from a collague going on holiday, involving a man making nightly calls to a lady subscriber, causing her great distress.
The case handler advised the lady by phone that he was handing her case to a collague, and said he would put her on the line to ontroduce herself.
When the lady with 'the voice' said hello, the subscriber became hysterical, screaming that this was the man who was calling her, and they should get the police while he was on the line!
Our colleague dined out on this story for months, taking the potentially embarassing aspect of it and turning it to her advantage as an individual capable of assimilating the vagiaries that life throws our way.
Times have changed - and not for the better it seems!