Either this is a universe in which zombies are a part of popular culture in the same way as in the real world or it is not.
If it is then it really makes no sense to NEVER have have the re-animated corpses of the show referred to as such. The truth is that 99% of people would think of a zombie as being exactly this...a re-animated corpse. It doesn't matter where the word zombie originally comes from or what it was originally used to describe in the same way that it doesn't matter that the word robot came from the word roboti, itself derived from the word robota, and did not in fact describe mechanical beings but rather biological ones. In the real world the day re-animated corpses start walking around, especially if they are also then consumed by the uncontrollable urge to eat living flesh and have the ability in doing so to kill any human they bite who will then also die and become a re-animated corpse, is the day we start calling those re-animated corpses ZOMBIES.
Therefore the world of The Walking Dead has to be a world in which zombies do not exist in popular culture in the same way as they do in ours as the re-animated corpses of the show are not referred to as such. The truth is that this is a lot easier to accept than the idea that the people who make up this fictional universe wouldn't make almost any popular culture reference at all. No talking about old tv or radio shows. No mention of any celebrities at all. No clothing that makes reference to such things. I know this is a serious world these people are living in but they're still Americans aren't they? These things used to be their bread and butter. Beth singing Hold On by Tom Waits and Beth referring to a DVD player are the only instances I can remember, off the top of my head, of anything being referred to that smacks of popular culture from these characters' previous lives.
I believe that the main reason this universe exists without zombies is that to have them even say the word without recognizing the ridiculousness of their circumstances, and the humor inherent therein, would truly be pushing the boundaries of willing suspension of disbelief for the audience....and the writers don't want that particular element of humor in the show. Which is fine. But no reference to all the crap we ingest on a daily basis just to get through the day....come on!