I have personal experience of obtaining Continuing Care (fully-funded NHS care) for both of my parents. It was a hard battle, but if your parent is in care primarily because of health needs, you have a good case.
You're right that the NHS and Social Services have different agendas and families can get stuck in the middle. It's a crazy situation - and the various agendas are always motivated by money somewhere along the line.
Tip: If your parent/relative is currently in hospital and needs to go into a care home, the NHS will be keen to get them out ASAP and will put pressure on Social Services to do so. However, neither the NHS nor Social Services can legally discharge your relative before a full assessment for Continuing Care has been carried out, according to the legal guidelines, AND you have been given every chance to appeal any decision to deny funding.
Tip: If your relative is already in a care home and paying care fees, and yet their primary needs are health needs, they should be assessed for Continuing Care. This should have been done within 3 months of them first going into care. Very often it's not though. You can ask for an assessment for Continuing Care - and you can request that it be done using the 'Decision Support Tool'. This is the full assessment. Make sure you attend this assessment, as you'll need to put forward as much evidence as you can to show what your relative's health needs are. Sadly, unless you (or another family member) do attend to fight your relative's corner, you're unlikley to secure the funding, as the whole process is such a shambles.
It's worth pursuing Continuing Care though. Very often you discover that the NHS and Social Services are acting illegally and they don't have a leg to stand on. As many families discover, the various authorities do seem to make the whole process as difficult as possible, but they cannot continue to break the law once this has been exposed.
I hope it's OK to post this link here: www.caretobedifferent.co.uk - you'll find lots more information on the site. It's my own site, and I now help families fight for Continuing Care.
Hope that helps for the moment.
Angela