I disagree. Statements like "if there are 10 [well mixed and otherwise indistinguishable] balls in an urn and three of them are red, the probability of pulling

I disagree. Statements like "if there are 10 [well mixed and otherwise indistinguishable] balls in an urn and three of them are red, the probability of pulling out a red ball is 30%" are absolutely falsifiable. An experiment showing that this statement is false is certainly possible. You're right that these are mathematical models and therefore simplifications of reality, but they are useful mathematical models only if their predictions are empirically valid. And if anyone came up with a more empirically useful version of probability, they'd be famous even if mathematicians refused to accept it, because all the scientists, engineers, gamblers, actuaries, etc who rely on the predictions of probability would make it so.