Actually, Trinity_Tx is right. Your error is that you confuse the cerebral cortex with the whole cerebrum. The cerebral cortex is just the "outer layer," while the 80% you cite is referring to the cerebral lobes underneath. See, for example, http://www.alzheimers.org/unraveling/04.htm. From the alzheimers.org glosary:
Cerebral cortex - the outer layer of nerve cells surrounding the cerebral hemispheres. [my emphasis]
I think the confusion arises when people look at a diagram of the brain and see the post label for "cerebral cortex"--and don't realize it's pointing to just the outside layer. (Sort of analogous to a picture of a cake that has an arrow to "Grey Frosting" and people think the whole cake is a blob of frosting. :-)
For example, here is the abstract of an article on a study done of boys with autism. Scans of the brain were done to determine volumes of each part, and the cerebrum was subdivided into cerebral cortex, cerebral white matter, hippocampusamygdala, caudate nucleus, globus pallidus plus putamen, and diencephalon (thalamus plus ventral diencephalon). The children with autism had smaller volumes of cerebral cortex relative to the massive white matter portions below when compared to the control group.
Michael Schiavo had Terri totally sedated the last time she had the tube pulled. Her parents complained about it because she was "too unresponsive".
According to Murray L. Barr and John Kiernan in the The Human Nervous System, 4th edition, page 221:
Each cerebral hemisphere has a mantle of grey matter, the cortex or pallium, which comprises about 40% of the weight of the human brain.
That is 40% each, for a grand total of 80%.
It does appear to me that different neuroscientists use the phrase "cortex" differently. Keep in mind however that the obvious characteristic feature of the human brain compared to other mammalian brains is the extreme folding of its surface, so that the top layers of the brain may occupy more volume than you would expect.
I would be extremely interested in reading the actual testimony of any neurologists called to testify in this case, to see how they are using the word.