Have you read the studies linking aspartame to changes in gut biome? For instance this one:

http://www.ncbi.nlm.nih.gov/m/pubmed/25313461/

You may be right about aspartame. I'm not an expert. Perhaps that study was also disproven.

But my larger point is that it's really, really hard to prove a negative to an acceptable standard. Particularly across all categories we care about, not just cancer and heart disease.

Have the biome effects been disproven too?