I think that the "made up stories" are probable actually false memories called confabulations, which are very much a feature of mid-stage dementia.
What happens is that the subconscious brain is trying to make sense of the fragments of memory left, so it takes these fragments, adds a load of other things (old memories, dreams, stuff seen on TV, conversations heard, etc etc) and spins it all into a false memory to fill the gaps in the real memory. Memory of emotions are remembered for longer than the events so the confabulations are often dictated by emotions felt at the time of the forgotten event
My mum thought that I was shouting and hitting her, although in reality it was the other way around. She was living on her own at the time and was frightened because she could not understand what was happening and didn't realise that the problem was her. She remembered the emotion and had fragments of memory of shouting and hitting, so a confabulation of me doing it to her was the way that her subconscious made sense of it.
People who are getting confabulations do not realise that the memories are false. They have no control over them and they seem like the real thing so it is difficult to manage it. If you try and tell them that they are wrong it usually makes them angry because they know that they are right because they remember it......
The usual advice is to just go along with it, but sometimes you just can't. I found I said things like "I'm sorry you feel that way", or even just "mmm....."