Science can disprove the link between autism and vaccines or reiki and healing, but there will still be people who believe that vaccines cause autism or in the healing powers of reiki. Why? Because they know, or more commonly, know of, someone to whom it happened.
Scientific American has a great article discussing this phenomenon: How Anecdotal Evidence Can Undermine Scientific Results. Money quote (but read the whole thing!):
The reason for this cognitive disconnect is that we have evolved brains that pay attention to anecdotes because false positives (believing there is a connection between A and B when there is not) are usually harmless, whereas false negatives (believing there is no connection between A and B when there is) may take you out of the gene pool. Our brains are belief engines that employ association learning to seek and find patterns. Superstition and belief in magic are millions of years old, whereas science, with its methods of controlling for intervening variables to circumvent false positives, is only a few hundred years old. So it is that any medical huckster promising that A will cure B has only to advertise a handful of successful anecdotes in the form of testimonials.
The scientific method came about precisely as an attempt to defuse this all-too-human tendency to fool ourselves. But unfortunately, many people would rather stay fooled.