I'm sorry for the distress this has obviously caused you. But I am afraid you are wrong. Your Housing Officer had a duty of care, in respect of the property AND a safeguarding duty towards your mother. That's the law. She would not have had access to hospital records, social work records, or anything else. What she did know is that an elderly and vulnerable person lived in a property, she hadn't seen her, and when asked the person living with her was evasive and refused to let her see the person, or to visit the property.
I am afraid that it is tragic, but in this day and age, elderly vulnerable people are abused - financially, physically and mentally. You might not think that there were any red flags, but honestly, from your own description here I can see lots of them! She was doing her best to ensure that your mother was definitely safe and well; and I am glad that she did, even though that upset you. If you truly realised how many abused elderly people are never spotted, you would be glad that she cared enough too.
When things go wrong - whether with old folk or children, the tabloids are always screaming blue murder about how people slipped through the cracks, and why did absolutely nobody notice, and all these "officials" should be sacked for letting it happen. But when they actually do do something, they get criticised for interfering. They can't win. But I would rather they interfered in 100 homes where nothing untoward is happening than the ignored a red flag, and some old person dies abused, starved and stripped of their money and dignity.