I am so sorry to hear of this great worry. Your mum's current situation works well. Someone wants to upset the apple cart to save money. You do wonder how they can sleep at night doing a job like that, trying to turf vulnerable people out of a place where they are safe by pretending that they have somehow 'got better' since they went into residential care. There is a phrase you may find helpful and keep repeating it to any of these numpties: A Managed Need is Still a Need. Your mum is clean, fed and content because she is looked after so well.
She has a high level of care needs - she cannot walk, is doubly incontinent and unable to wash herself, dress, prepare food, etc. etc. So she cannot survive without constant supervision and support. You cannot be forced to be her carer. They cannot make you take her home. If this assessor thinks she doesn't need to be in residential care then what is the alternative being proposed? A sheltered flat where she sits all by herself waiting for carers to come in 4 times a day, and then being left for 10 hours on her own overnight? How safe would she be then, unable to walk, unable to get to the toilet?
The issues I would emphasise in fighting this ridiculous assessment are:
Safety, health, dignity and respect, socialisation and freedom from fear and loneliness.
In addition, a reminder that your mum suffers from a progressive illness. If she needed residential care a year ago, she needs it even more now. People don't recover from dementia, they just improve their health and wellbeing when they receive the optimum support from a team of people 24/7. Since the only team available 24/7 in the community are family carers, you can see where they want to transfer the burden and costs. Don't let them try it.
P.S. Having read your message again, I see that your mum is in a nursing home. Is it perhaps the nursing side of things that is being challenged? Perhaps the assessor is saying that she only needs to be in a care home and doesn't have special nursing needs?