Yes, chlorine bonded to an organic molecule is often called organic chlorine to distinguish it from the many inorganic chlorine forms there are. Inorganic chlorine atoms are not uncommon in nature. There is nothing misleading about it.
I don’t see it as particularly misleading to call chlorine that is covalently bonded to an organic molecule ‘organic chlorine’. I mean, what else would ‘organic chlorine’ mean, in a chemistry context? And it’s an important distinction: there is a real and large difference between the chloride ion in table salt (found everywhere, including as a necessary part of living cells), and a chlorine atom attached to an organic molecule, which is almost never naturally occuring, and has very very different effect. I think it’s much more misleading to compare chlorine in table salt to the chlorine in, say, PCBs or TCE.
And enough chlorine-containing organic molecules have proven to be carcinogenic or toxic, that caution in dealing with any chlorine-containing organic molecule is justified. Whether there has been enough study of the Splenda molecule to overcome that caution is a different issue, but in general, organic chlorine is at least a yellow flag.
I’d say it was a myth too if it was going to cost me business. Seriously, that’s no argument if there was countervailing evidence—and there seems to be.