Yes, making things up is part of dementia - its called confabulation. Your mum is not doing on purpose and wont even realise that she is making things up. What happens is that your mum has lots of gaps in her memory and the subconscious brain is filling them in with false memories made up from things from her past, things people have said, stuff seen on TV, dreams and a large dollop of imagination, all mixed up together. Its done to try and explain and fit together the bits of memory that are left, even though we know that its not correct.
Dont try and correct her - it will only upset or anger her because, you see, she remembers what she says and to her the false memories seem like the real thing..........