Divide and Conquer 3D Convex Hull
The paper explains why the number of comparisons is $O(n)$ in the next few sentences immediately after the statement you're asking for a justification of.  Just keep reading for a few more sentences, and you'll immediately find the justification.  As it says,


  "First of all, we notice that each type 1 comparison definitively eliminates one edge ...  Since the numbers of edges of A and B are at most $(3p-6)$ and $(3q-6)$, respectively, the number of type 1 comparisons is bounded by ..."


and so on.  So to find the explanation for that statement, just continue reading a few sentences onward.



And, as the paper says in the introduction,


  "[our algorithm]" is based on the property that the number of edges of the convex hull of $n$ points is at most linear in $n$."


Therefore, your examples are not possible.

See also the 3rd paragraph of Section 4 for more elaboration ("It is a crucial observation that...").