One thing to consider, humans are omnivores that are from herbivorous ancestory, our digestive systems are designed for things that carnivorous animals (dogs, cats) cannot take, cannot digest, or would pass through without even a single benefit.
Artificial sweetners have been known for many years to cause or lead to, or assist in symptoms among some or few people. Knowing someone involved with the creation of splenda, I also know that as far as safety to humans, it is better than its predecessors. Some sources say that saccharin is better than its replacements as far as safety, this was why a sugar based sweetner was created.
I know that side effects listed on modern products by law have to list all unusual symtoms by the test group during that period of testing regardless of what caused it, or if it may have been imagined. This is why many medicines and food products say that they may cause symtopms that have nothing to do with the product, if it happened in testing it must be listed.
Think about it, Im sure enough sugar will cause serious harm to a dog or cat. Stevia is a natural sweetner, but its not safe for them either. Something to consider, sugar free doesnt always mean it is unsafe, if its not sweetened it may be safe. Just consider what all of the other ingredients do or dont do for a carnivore. Sugar is added to many cheap dogfoods to make it more appealing to dogs, why its a proven fact that dogs have a sweet tooth compared to cats, the companies take advantage of this.
Ive heard of the problems that the sweetner this post started about causes, it is most definitely dangerous to dogs and cats, more so (even in tiny amounts) than some of the others.
Some plant based products are dangerous to some species where as some are not effected and can eat them. This has been a defense by almost all plant species that have survived a long time. Even some animals do this, human history has only gone back about 6000 years in Australia, but the venom in the Sydney funnel web spider evolved to be its most deadly to humans, and apes, none of which evolved, or lived naturally in the continent. Also consider that male spiders are almost always the smaller, and harmless sex, the Sydney funnel web male is the only one with this particular venom so potent to humans (the male spends so much time wandering during mating season, among one of Australias highest human populations, this is evolution in action).