If I'm reading that correctly, they say there's no problem at the current doses, no?

It can't have a similar metabolic effect to sugar. For one, it's a peptide, not a carbohydrate. Also, in the quantities it's consumed in, there are very few calories.

Now, for phenylketonurics it's problematic, but they have severe dietary restrictions anyway.

The only problem I'm aware of with aspartame is that consumption of any sweetener is associated with weight gain, possibly due to changes in the brain's association between taste and calorie intake.