If one is an underling and notice that the secretary only greets those with some responsibility and otherwise never replies to someone who says "Good morning" anyway every day, do you think that person should take issue? I'm trying to think from the secretary's point of view also and I wonder how tiring could it be to greet around 100 people every single day?
My own opinion is that they should reply once in a while and they are being extremely rude by never replying.
Additional info: when one enters the office, the secretary is less than two meters away, so it makes it kind of awkward to not say anything. It's not like she might be five meters away or more.