It is pretty much like Ernie said, this is an apples-to-oranges comparison. That does not make it false, you can have a logically and statistically flawed analysis and still arrive at the correct conclusion in spite of the methodology, but you can also fool yourself into believing a result that is not correct.
Dr. Liau is the same as you, looking for answers to an unsolved problem, but she doesn't have access to the necessary data to state conclusively that the patients are alive because of the drug and not some other reason. Every researcher chases a hypothesis until they find evidence that disproves their belief, at which point they discard that hypothesis and follow a different path. Belief in something that is later disproven (or can't be proven to a statistically certainty) does not make the researcher a fake; it makes them a scientist.