I don't think there's any reason to believe it does not literally mean the base of the model. If it meant the FAQ'd definition of base, which refers to the entire silhouette, then there's no reason for the second sentence to even exist. They would have just said "1/3rd of the model" and been done with it. On top of that, if the second sentence does exist and base means entire silhouette, there's no reason to call out height as a separate requirement. That's how I'm reading it anyway. I was always under the impression the definition of base was only FAQd for base to base contact and didn't affect any other contexts. Consequently, yes, I believe that cover which starts above the ground does not provide cover.
It's an entirely logical position. Except CB. @tox apparently this *does* need to be added to the FAQ.