Is it okay and safe for someone to scuba dive even though she can't swim?

Jacques Cousteau one of the better known inventors/developers of Scuba routinely and successfully took people who couldn't swim underwater with his equipment. This gear, even if in perfect condition would probably be avoided by divers given the choice of a modern regulator. He also took old people to very deep depths on their first dive. Whilst none of them died we probably wouldn't consider that to be the best plan or criteria of success.

I suppose if you can breathe underwater with your SCUBA your poor swimming skills is not such a problem as you won't drown. On the other hand being confident and comfortable in the water is very important in diving and as a result all diving accreditation including PADI BSAC and CMAS have minimum swimming requirements. These are not normally very big distances either. As a diver I have often had to swim on the surface a long way without breathing from my cylinders so it probably helps to be able to swim. I would say that these organisations who make it their business to train people to dive probably know best, so if they suggest a minimum swimming ability it might be wise to achieve that before swimming straight down...