Why is a mild earthquake often mistaken as dizziness or vertigo?
Having experienced many minor earthquakes (Mag 3 to 5 in the East African Rift Valley, Samoa, Solomon Islands, Philippines and Indonesia), and one major life-threatening earthquake (Magnitude 8, Nepal), I can make a few personal observations about physiological reactions.
First, You are quite correct about the body picking up any swaying feeling, and interpreting this as dizziness. I was in an 11th floor hotel room in Bangkok when an aftershock of the Aceh earthquake occurred. My first thought was "Did I drink too much beer this evening"? I wasn't alone. When I opened the door into the corridor, the occupants of nearly every room were looking out and wondering much the same thing.

Second, after experiencing a big one the body becomes hypersensitive - conditioned to pick up vibrations that could be the onset of a major quake. Now, at the onset of any vibration, my brain goes straight to "how big is it - should I run to the nearest exit"? This response is now much faster than the sensation of dizziness. Also I now pick up many vibrations that nobody else around me seems to notice. 

Thirdly, I am not sure I agree with you about vertical motion being the trigger. It seems to me that lateral motion - moving one's feet sideways relative to the head, creates a slight imbalance, which the ears interpret as 'dizziness'.