I think your phrasing is much too strong. Research shows that about 8% of migraine sufferers self-report that they believe that aspartame triggers their migraines [1]. Placebo-controlled studies show mixed results, and only at high doses (Along the lines of what you'd get from drinking 10-14 cans of aspartame-sweetened soda per day), and only for a subset of the migraine-suffering population, and only for those who don't suffer from cyclical migraines or status migrainosus [2].

1: https://pubmed.ncbi.nlm.nih.gov/2708042/ 2: https://headachejournal.onlinelibrary.wiley.com/doi/pdfdirec...