The hospital can specify that a carer or family member has to be present because the need is considered non medical. It's their job to provide nursing care but that doesn't include the supervison of the behaviours that come with dementia. The reason why this may seem surprising is because from your description, her needs are at a level that she would more usually be in a nursing home or have a very high level of home care, in which case nursing home carers or a main family member carer, would be expected to be present. It might sound like splitting hairs but nursing home carers or community carers are social care staff, not NHS . It's not so much that the nursing staff are saying it's a family responsibility - their point of view is it's not their responsibility, they are not set up to provide constant supervison to adults and can only meet her medical needs. So if the only people involved are family members, then by default family members have to sort it.
Contrary to popular belief, social care don't try and dupe family into doing things to evade responsibility. The principles underpinning social care legislation state that family are responsible for family, and that the state should only intervene if all avenues for support from family has been exhausted. That's why social care support is only offered if family explicitly state that they can't/won't, or if there is no family to trace.
I'm not saying any of this to justify it; the system doesn't, in my view, recognise societal changes where this level of family care is no longer the norm, nor practical, due to changes in women's employment for example. However this is the basis for the decisions that are made, and the reason why, to get the care your MIL needs, you need to stress to the hospital:
What the limitations are of family support and why
That if her needs are considered non medical & supervisory only, that you want an urgent social care assessment for her holistic needs to be addressed, to ensure that her medical treatment is not compromised.
It's a horrible situation and I'm sorry if my post comes across as blunt, I'm not in agreement with the system I just hope the explanation can help with where to direct your efforts.