Actually, the Black-Scholes formula is innocent. Sure, it assumes that stock movements follow a standard distribution, but that's not as big a sin as is being made out in the article. The formula computes the fair price for an option contract. Such a contract gives its owner the right (or "option") to buy or sell some asset up to a future date (the expiry date), at some given price (the "strike" price). The formula uses the following values:
1. The time remaining until the contract expires
2. The current price of the undelying asset
3. The strike price (the contract gives its buyer the right or "option" to buy the asset at the strike price)
4. The risk-free rate of return on cash (return that could be earned by putting your money into, say, treasuries rather than stock)
5. The volatility of the underlying asset.
At the time the contract is written, the first four of these values are known (assuming of course that the risk-free rate stays constant, which is pretty close to a sure bet). The LAST value is the problem. It says how much the stock will fluctuate, between the present time and the time of expiry. This is unknown, because, after all, it requires knowledge of the future. Usually, PAST volatility is used in its place, going with the assumption that the stock will behave in the future the same way it behaved in the recent past.
If the stock suddenly becomes very quiet, and stops fluctuating, the buyer payed too much for the contract, on average. If the stock gets very wild, the buyer got a bargain, on average. In either case, the contract buyer and seller guessed wrong. They should have used a different volatility to price the option.
Of course, stock fluctuations do NOT follow a normal curve, after all. And option traders do NOT follow Black-Scholes exactly either (see "volatility smile"). But the much bigger flaw, I think, is lack of clairvoyance. The formula requires knowledge of the future.