I actually consider that a much more nuanced (or muddled?) statement.
While it is politically dubious of them to comment at all, the impression I get from that statement is that their interest in the case only extends to their interest in supporting the legal principle of gillick competence.
They aren't going any further than supporting a child's right to have their views given due weight in any decision being made about them. We have a fairly long standing understanding in this country that for medical treatment, there is an assumption of competence from age 12.
I read the statement as basically stating that any child from age 12 can consent to their treatment without intervention from an adult. We support that even when it is controversial treatment. but expect adults around them to support them in making decent decisions.
I would have expected more emphasis on safeguarding and ensuring the medical options are appropriate and safe given the fact such young children CAN consent to treatment. It would have been better if they had said nothing at all though.
12 year olds can go on the pill without parental consent. The fact they have the legal right to do that doesn't ignore there is a much bigger question of how they got there in the first place. You would hope children's charities would be more robust on that side of things.