In the later stages of dementia, a person gets details mixed up and sometimes fabricates things from fragmented memories. In the field of Psychiatry there is a name for this mental process called "confabulation", which is defined as: Filling in memory gaps with a falsification that a person believes to be true. The dementia afflicted person absolutely believes without question, that this memory is complete and intact. Sometimes these "memories" are plausible explanations that sound reasonable and other times, they are absolutely preposterous. Because the belief in these is absolute, it makes no difference that they are illogical, impractical, or even impossible.
Visitors of the person with dementia may have a perfectly normal conversation without ever becoming aware that a confabulation has been verbally expressed to them. They can be hard to spot even when you are aware of them and are expecting them. My mother may tell me that she went on a scenic bus ride on Sunday and describe it in some detail, when in fact she hasn't taken a bus trip for several weeks and hasn't left the assisted living building since that occasion, either. It makes for challenging conversations and awkward circumstances sometimes. This is not to be confused with delusions, which can seem very similar. In this instance, she intended to go on the bus ride, but missed it and did something else, later forgetting what she did instead. She probably spoke to someone later who did go on the bus ride and learned some of the details which then became her own memories of the trip.
It's natural to want to question comments that don't ring true and suggest alternative possibilities to correct a memory. It rarely helps to clear anything up and actually adds more confusion for the person having the memory trouble. When these confabulations are harmless falsifications, it is best to ignore them and accept them as though they are factual. The person telling the story absolutely recalls every detail of it as a fact and clearly remembers doing whatever their brain fabricated to complete the story. They aren't lying, because they are relating the truth as they recall it. They will argue if challenged about these memories. That is another good reason to just let it go.
When a confabulation isn't harmless, it can cause all kinds of problems. Perhaps one of the worst examples is when a confabulation involves a caregiver in a sexual situation with the dementia patient. In this scenario, the person telling the story absolutely believes every detail and can be very convincing if they are telling the story to another resident in the assisted living community. An innocent caregiver can be characterized as an opportunistic sexual partner and that can lead to abuse allegations or create fear in the other residents. These confabulations absolutely must be addressed delicately, but directly, and it will be an awkward head-on confrontation. It will take a multiple person intervention to try and purge this error in memory. It may never be completely eliminated, but you may get the person to stop talking about it. In time the false recollection may fade away and be forgotten.