This appears relatively safe. Even accident statistics produced by groups pushing for regulation are pretty mild. Industry regulation is a pretty politicized process, creating plenty of pressures to inflate injury rates -- so if even those are small, it's probably safe. Those sites (such as this one) only have a minor injury rate of 0.001%. Realistically your wife is more likely to be hurt driving to the location to parasail and showering afterwards than in the actual event.
"Statistics" that give raw counts without perspective are useless. Is 59 accidents in 20 years a lot? A little? It informs very little regarding the risk of accident. 59 accidents in 59 trips would be 100% chance of injury. Without knowing the ratio, the number of accidents is meaningless.
(A note, I just edited this after three years and I have no idea where the link was originally intended to go)