Both Black-Scholes and binomial model assume that there's no risk-free arbitrage in the market. But that sounds like a very weak condition.
If a trading scheme makes you gain 100 dollars with 99% probability and lose 5 dollars with 1% probability (starting from 0), this is not risk free but it will be surprising if such an arbitrage opportunity exists without being exploited.
So, either a) Black-Scholes does not make accurate predictions about the prices of derivatives, or b) statistical arbitrage of the type mentioned above does actually exist in the Black-Scholes Model. Which one of the two is correct?