As is your right, however such a broad, sweeping statement isn't really credible, much like the anti-smoking propaganda out there.
Sucralose and stevia have NOT been linked with cancers, or any other serious side effects.
Boresha Research
http://www.benthamscience.com/open/toobesj/articles/V002/101TOOBESJ.pdf
Aspartame has some questionable science behind it as far as cancer goes, however it has been shown to affect the endocrine system negatively.
I see no problem with avoiding artificial sweeteners for the sake of living more "naturally", however to claim that they all have been linked to really bad things isn't really accurate.