Four groups lodged concerns in this case: anonymous people (presumably other parents), schools, health care professionals and the police.
One of the concerns raised by HCPs was that the mother was informing them that her child had a diagnosis of gender dysphoria, despite no such diagnosis ever having been made. That would be where the Munchausens by Proxy worry comes in.
That surely raises concerns about the proposals for allowing self identification - anybody who says they are trans is trans, or in the case of young children, anybody's whose parents say they are is.
The NHS classes being trans as a medical condition. We know it involves treatments up to and including surgery. There is no other medical condition you can self identify as having. If we allow people to self identify into having a medical condition, it creates a massive loophole for people with Munchausens to exploit.
For the woman in question, I know how it feels to go up against an authority figure because you disagree over your child (I am sure many people do). The conflict between different groups over trans ideology (accepted it seems very greatly by SS but far less by the NHS) is surely itself exacerbating disagreements between parents and professionals, and increasing feelings of isolation and victimisation, because one side is uncritically backing whoever calls out trans.