Was this rumor about Salieri contemporary with the era of Mozart? I am pretty sure this conspiracy theory never existed until the play/movie (I forget which came first) was written.
They had no toxicology test back then, and competing accounts exist. The lede article refers to a modern physician who thinks Mozart suffered from trichinosis contracted from undercooked pork. Have any relics of Mozart been chemically tested? Anyhow, many diseases could feel like “poisoning.”