How do EMH proponents explain Black Monday (1987)? On Black Monday (19 Oct 1987), the Dow Jones Industrial Average fell by 22.6%. How do proponents of the Efficient Markets Hypothesis (EMH) explain this event?
Do they actually claim that the intrinsic value of the DJIA fell by 22.6% that day? Or do they have some other explanation?
Different proponents of efficient market hypothesis  (EMH) will have different explanations because EMH does not say which fundamentals/variables should drive prices. EMH just states that prices reflect avaiable information but it does not say which avaiable information is important and which isn't.
There are actually several versions of efficient market hypothesis  and answer might be slightly different for each of them (in details but not much overall). However, generally speaking efficient market hypothesis is not theory about why market prices fall or go up.
Efficient market hypothesis is a hypothesis about informational efficiency of market. As explained in Miskin &amp; Eakins, Financial Markets and Institutions 8th ed. pp 158 :

Efficient market hypothesis (also referred to as the theory of efficient capital markets) ... states that prices of securities in financial markets fully reflect all avaiable information.

authors further explain:

The efficient market hypothesis views expectations as equal to optimal forecasts using all avaiable information. What exactly does this mean? An optimal forecast is the best guess of the future using all avaiable information. This does not mean that the forecast is perfectly accurate, but only that it is the best possible given the avaiable information.

Consequently, EMH does not say why prices go up or fall. It just says they contain all avaiable information and also refers expectations of future prices and again just says that these expectations will be the best forecasts given all publicly avaiable information. It does not even say these forecasts will be correct as they are just forecasts.
In order to say why prices increase or decrease you would have to combine EMH with some asset pricing theories that actually try to explain stock price behavior. For example capital asset pricing model (CAPM) could be used to explain what drives returns (which are changes in prices) and CAPM can be modeled together with assuming EHM but it can also stand separately. Furthermore, CAPM is just one example of a model that tries to explain asset prices, there are many more and in principle all can be combined with EHM.
For example, Stout (1997) uses EMH together with CAPM to show that in such model stocks might be sometimes undervalued (when there is large amount of uncertainity). So Stout who is proponent of EMH (at least to the extent that he uses it in his research) could say this might be because market undervalued stocks due to uncertainty.  The point here is that in order to know what proponents of efficient market hypothesis think about what caused Black Friday you need to enquire about what asset pricing model they are using. Different proponents of EMH will give you different explanations because being proponent of EMH does not mean you are necessarily 'married' to single asset pricing model. For example, if someone argues stock prices are given by present value of their dividend (something that could hold whether EMH holds or does not hold) would say that Black Friday was caused by expected net present values of dividends dropping and EMH would just state that those expectations were formed by all publicly avaiable information.