That's an overstatement of a mathematical theorem. Arrow's theorem says that for approval voting, yes there are some cases of people's preferences for which one of those conditions fails. Nobody is claiming that approval voting satisfies all of those conditions, so nobody is provably wrong.

People are claiming that approval rating works better than first-past-the-post in many important cases, such as introducing a moderate candidate into an established two-party situation. Arrow's theorem does not contradict that.