You mean, what you want to be true?
Not necessarily. You almost never have control over the process of filling up or reconstructing your memories. Unbeknownst to you, the process operates probabilistically. Given your past experiences and knowledge, your memory system gives you the most likely thing that could have happened to help you fill any gaps at the time of retrieval. Most of the time the final product coincides with what actually happened, so it is true. But sometimes it does not, in which case we talk about false memories. I think most of our memories are reconstructed in this way, and many of them are false, we just don’t notice.
All of this made me think that when we imagine things, we also imagine how things could have occurred in the past. Say you were crossing the street and almost got hit by a car. You can’t help but imagine what would have happened if you did get hit by the car. We just slip into that kind of imagination.