I suppose it depends upon which description of truth you mean. There is truth in sincerity and also truth in actuality. I generally refer to the later when meaning truth but have used the other as well.
To clarify there have been quite a few studies involving memory reliability and decay over time. One particular case study that comes to mind involved a nature hike with the participants instructed ahead of time that it was an experiment to see how many details of the hike they could remember after a period of time. They were all wearing head cams to record what they saw. Unknown to them this was actually a study of how the mind might perceive events that related more towards a paranoid basis. Along the trail they were travelling a false crash scene was placed with a man in a military uniform standing near it. As they approached it the person leading the hike explained that there was a crash here and the military came and was keeping them away from the site and that they shouldn't get near it and just needed to keep going as the military didn't want anyone around it. After the hike was over the camera data was taken and they were instructed that they would be contacted later to see what they could remember (I think the period of time was one month but it could have been as long as three months).
After the appropriate time, they were later asked what they remembered. Some of them remembered approximately what they saw, with varying degrees of detail. Interestingly, some of them remembered an alien crash site and US military soldiers pointing weapons at them and other such fantastic events. They were debriefed under a lie detection system and although as elaborate as some of their memories were, it was determined they were not 'lying'. One woman remembered "one of the soldiers" pointing a weapon at one of the other hikers and her getting between the hiker and the soldier to protect him. In fact there was only one man at the fake crash site and he didn't have a weapon and the recording of the woman's head cam revealed that she had never even seen the man nor did she attempt to protect any other hiker. She wasn't 'lying' though, she was truthfully telling what she remembered.
The general conclusion of the study seemed to suggest that in a rather short time after any event, that the brain would rewrite the data it had regarding the matter and then store it into long term memory (possibly altering it more even then). It further suggested that eye witness testimony after any length of time rapidly decreased in reliability.
Now to get back to my original statement, the actual truth was that they took a nature hike by a man standing by what looked to be some sort of wreckage. What some of them remembered and later revealed truthfully as what happened was far from the actual truth even if they were sincere in telling it.