Yes indeed, including in some cases changing the temporal order of events based on reason or new data. For example, I once misheard a drinking mug shatter on the floor before it slid off the kitchen surface.

But reason corrected the memory.

https://hilo.hawaii.edu/~ronald/310/310-Dennett-MultiDrafts....

I'd like to add that I think 'living in the moment' is powerful and useful despite not being literally true because it points to something real and important.