While she is here and the authorities are aware and not removing her I believe she has a moral right to equality with other children in her community
Morally you may be right. But this isn't a moral issue. A service as huge as the NHS cannot be run on morals, or take morals into account. It has to be run as a business for the benefit of the many rather than the few.
While she is here and the authorities are aware Except the authorities weren't aware, not until last month. She was being treated with physio, received a lot of NHS funded care that she was NOT entitled to, right up to the point that the operation was mooted. It was only when the Trust asked at that point for confirmation of her status that the fact she was 'illegal' came to light. Again this is the fault of the parents.
If she were to be treated now, then a dangerous precedent is set - "Leave everything to the last minute, then when you are found out, threaten the NHS with a lawsuit, and you'll get what you want"
That is why I believe that this case should be resolved by charitable funding and not by the NHS.
This child was born here and sustained the injury here. It is not health tourism I'm not convinced. The family have had 3 children 'on the NHS' since 2009 - since they have been 'illegal'. If they wanted to be a part of this country, a part of the UK 'Community' with all the benefits that it brings then they should have applied for LTR back then. Not applying until this year after a consultation with an Ambulance Chaser makes them the very definition of health tourists - they didn't bother until they were asked to pay.