Can you expand on how the Volatility Smile demonstrates that traders model fat tails in their options pricing strategies. It wasn't clear to me from the wiki page you linked.
BS does assume a normal distribution; the point is that people do not strictly take the output from BS and say "tada, here's the price."
Assume that you want to buy an option on Apple stock - 3 months in the future. Assume that price today is $500. If you want to buy an option with strike=500, you will pay 50 vol (BS as a formula will just convert the price in vol terms into a dollar cash price). But - if you want to buy an option struck at 400 - you might pay 75 vol. And if you want a 300 strike - it will be 100 vol.
As you see, volatility will RISE the further you move away from spot price (ie where it is today). So while BS calculation assumes constant volatility to convert vol to dollars, traders always ask for higher vol, as you move out to less likely scenarios. That is how they deal with the world being non-normal. It really is options 101 - so any writer who talks about BS assuming Gaussian probabilities is either lying or doesn't know anything about the subject.
It's just a formula to convert volatility to a dollar price of an option. But the actual vol surface that people use is anything but Gaussian. So the job of the trader is to construct a vol surface. However in order for 2 people to trade an option, they have to agree to a cash price - which is when BS is used. But the entire trading universe revolves around vol surfaces.
Think of it as making a painting. BS is just a single paint pigment - whereas the painter will take 20 pigments and mix them up to produce millions of colours. So to accuse those who use BS formula of assuming Gaussian probability distribution is akin to saying that painters use one color to paint.