Perhaps it's not a case of people really believing that dead people have more cognitive abilities than the "living". This again is one of those tricky morality/judgement issues which is far beyond the scope of this simple survey.
Perhaps the cognition rating was more in a social context. Death, is a very critical part of live. It's almost a rite of passage in some ways. After death, you leave behind your legacy. If you're a leader, a successor might pick up the torch and rally the troops in your memory, so in that sense, a dead person's memory/personality may be more "alive" than one in a persistent vegetative state.
Case and point, Ariel Sharon. (I mean no offense to him) Had he passed on, it may even have energized his party/cause etc. Instead, being in a coma has actually been worse for him. It's hard to inspire others in the "memory of" when that person is still breathing. Even worse, when someone comes around, their cause, work etc may no longer be relevant if it's after a very prolonged period of time.
I think the article oversimplifies the issue. Chalking it up to "religious" and trying to correlate that with people thoughts seem rather random. Perhaps "religious" people may be thinking more from a societal context? Nevertheless, if this is a serious effort, I hope they have follow up articles with more data that really helps identify this. It's not just an interesting topic in that it defines death, but it reveals more about the inner workings of the more complex parts of our cognitive system and how we develop our "values" (no pun intended).