Did they? Because they've also shown the zombies have no biological "need" other than brain activity and even then only on the most basic level. We've seen zombies who've sustained massive damage to internal organs and even some with missing lower torsos so clearly they have no biological activity or "need" to eat.
In the pilot Morgan Jones wife kept returning to his house and tried to open the door. Doesn't this imply they have some basic memories?
Also we see some of the zombies returning to familiar places e.g. the church and sitting in the pews.
It does seem that the Walkers have some "basic" memories but calling it a memory may be over-stating things. It's more likely they have autonomic impulses. Memory implies "I remember this, I am going to go do it," An impulse is more like breathing or your heart beating neither of which you have to consciously or remember to do. So I think with a lack of anything to eat, a noise to follow, or whatever the Walkers sort of go to some basic form what [was] normal.