Distillation followed by filtration through activated carbon should render the water safe.
Respectfully... any reference to an authority saying that?
Cant find a link, but I have read this in a Royal Navy engineering textbook. something like
"drinking water on board HM ships is normally produced by the distillation of seawater. In the open ocean nothing else is required. Distillation removes not only salt but also other harmful material, viruses and bacteria. However in ports, rivers and estuaries, the sea water is liable to contamination by oils and solvents and depending on the boiling points, these materials may pass through the water maker. The distilled water should be additionally treated by passing through activated carbon filters in such places."