Okay thanks for confirming you don't know what you're talking about. Black scholes is options valuation and never used in 409A valuation. You can't just make stuff up, you have to justify it to your auditors.
'never' is wrong, depending on your meaning. It's definitely used in many 409A valuations. Typically a 409A will use a couple different approaches to come up with the initial valuation -- it will look at the discounted cash flow, the value of assets and liabilities, and generally will look at 'guideline companies' and their public valuations or cash value upon sale. Once one or more (often times all) of these methods are used for the initial valuation, the value is fed into a Black-Scholes model. That price (after applying discounts for non-marketability) is used as the fair market value for the common stock.
As for real world proof of Black Scholes being garbage, it doesn't get any better than Long Term Capital Management.
Edit: people buying/selling options are of course performing their own pricing operations. They don't care how the market price is determined, since they believe their model is the best and gives more accurate prices than anyone else.
Edit 2: furthermore, to properly price startup options, you need to account for their 'random-expiration' nature: we have no idea when Uber will IPO. this makes it difficult to use traditional option pricing models which have fixed maturities (you can take integrals over the model's results at each possible maturity). additionally, choosing a discount rate is hard when realizing that most employees are not well-diversified, unlike the investors/funds that the traditional models are written for
While neither are great, binomial is better for American style options than BS.
I guess you could choose an arbitrarily distant expiration date, but my bigger point was that while BS is clearly not going to give perfect results, the results are reasonable enough and transparent enough to justify their use for tax purposes in lieu of actual market prices.
As for 409A valuation, I've never heard of an auditor seriously examining it or questioning its validity. It's mostly the "valuation expert" says, "What value do you want for 409A?" You tell them, they ask to see the books, and then say "OK I can sign off on that."