Exactly that. We may be able to recall our reasoning if we try to, but we're likely to throw in a few extra false justifications on top, and to forget about the other side.

I suspect it's more likely that we won't remember it at all; we'd simply increase the association between the thing and goodness and, if looking for a reason, will rationalize one on the spot. Our minds are very good at coming up with explanations but not good at remembering details.

Of course, if your values and knowledge haven't changed significantly, you'll likely confabulate something very similar to the original reasoning; but as the distance increases between the points of decision and rationalization, the accuracy is likely to drop.