My question is - should I have refused her travel?
There was an article on Today Tonight or AcA can't remember which with a very similar story where some old fella came in a bought a fare to somewhere and when he got there his dementure kicked in and he wandered the airport for a few days until someone realised that they had seen him circling and got security to check things out. The report slammed the agent and they went in to her store and stuck a camera in her face and grilled her as though it was all her fault.
If a person wants to buy travel, that is their business, you are not there to make judgements about the suitability of their health to travel. As a parallel example, should a motor bike salesman be responsible if he sell a bike to a 21 year old male who duely wipes himself out two days later doing some crazy stunt? I think not.
This is a part of the bigger problem with society as noone want to be responsible for their actions. You acted as requested completely within, I would assume, the law. I know we are talking about some old lady with mental issues but the crux of the matter is that it is not your fault nor should you have to fix it.