The prove for the claim is trivial. Words on the Swadesh list will show little correlation between meaning and phonetics, save for exceptions like mama. If there is a hidden correlation, then because the relation is more complicated.
EDIT: A weaker Argument would be constrained to a single language of a single speaker. I guess that's more or less what you mean. It's not quite clear what you mean, though. phone, word and set of semantics are not well defined as far as I know. That's in essence the same claim as you attack, if, whatever you refered to, was a response to a failed attempt trying to explain meaning from phonetics. Which would be called inductive reasoning, i.e. experience. The smallest constituent, of speech, the phone, ordered in sequences, is not enough to explain meaning, or to learn language.