Mindfulness is supposed to be focused on the Four foundations of mindfulness, for purposes of traditional mindfulness practice. Mindfulness limits our awareness to a narrower set of objects of awareness. So the idea that a person being mindful must recall everything said and done perfectly and cannot forget anything, is a myth. We can forget things but be aware of the present moment, despite being able to remember the past, and plan for the future, when we stop being powerfully aware of the present.
It’s true that remembering the past and thinking of the future are different to being mindful in the present.