This is a great question and you are right that our memories are not passive but very active. Many scholars from different field have been working on this topic. Here are two examples of how our memories are constructive.
First, since our minds are not perfect. We know this better...
as we get older. For this reason what we do often is readjust our past memories to interpret what is going on now or what we expect will happen in the future. This fact makes our past memory constructive. This happens to all people.
Second, if there any damage to the head, particularly in the prefrontal cortex and related brain areas, some people have what we call confabulation. These patients have false recognition of people and events, and even more they claim (incorrectly, of course) that new information is something that they have already experienced. In short, our mind have an interesting way of constructing things that we have never experienced.