My question is - Wouldn't it be better to "engage" the person and offer a mild correction to what they've said than to just "go along" with what they are saying. By engaging aren't you stimulating the person's mind and thought process for whatever it's worth even though there might be a slight disagreement afterwards?
None of us wants to freely accept that our our loved ones are drifting away into a world of their own. That’s why this forum exists—to help us caregivers through it.
Enjoy your time with her in her world.
What you have to understand is that the person is right. What is going through your mother's brain, her version of events, is in fact what is going through her brain. Your problem is that it is different from reality.
The idea of engaging is to connect with your mother's version and then, through questioning and listening, figure out the route from her version back to the real one, if possible, and worthwhile, or to whatever keeps her safe and reassured at least.
You say this is about "things which happened." What sort of things?