There's a big difference between the covalently bound chlorine in Splenda and the chloride ions present in salt. Chloride, like many other ions present in the electrolyte fluids in our bodies is essential. Free chlorine, which exists as Cl2, is toxic--just ask anyone around a public pool where they use cylinders of chlorine gas to chlorinate the water.

According to the Splenda website:

SPLENDA® is the brand name for the ingredient sucralose. It is made through a patented, multi-step process that starts with sugar and converts it to a no calorie, non-carbohydrate sweetener. The process selectively replaces three hydrogen-oxygen groups on the sugar molecule with three chlorine atoms.

They also have a completely synthetic way to make Splenda (which shows up in their patent) that, of course, wouldn't start with sugar but is probably much more expensive.

Chlorine is present naturally in many of the foods and beverages that we eat and drink every day ranging from lettuce, mushrooms and table salt.

This statement in itself is a little disingenuous as they are equating different forms of chlorine. Most of the chlorine you ingest is actually ionic chloride from salts.

In the case of sucralose, its addition converts sucrose to sucralose, which is essentially inert. The result is an exceptionally stable sweetener that tastes like sugar, but without sugar’s calories. After consumption, sucralose passes through the body without being broken down for energy, so it has no calories, and the body does not recognize it as a carbohydrate.

If indeed all of the Splenda passes right through your digestive system, then it is an ideal artificial sweetener.