Additionally, items which digest to glucose trigger insulin production. Aspartame has repeatedly been shown to not. Most other low calorie sweetners, additionally, have not as well.
Saccharin had one study that showed a correlation, however, several other studies did not.
However, protein does: http://www.ncbi.nlm.nih.gov/pubmed/1946186
In reality, they're surely still eating processed things, but they THINK they aren't, and placebo is all it takes sometimes.
