What I read is that, although Boeing issued a memo regarding this problem and called for pilot training on the issue, they (nor the airlines) did NOT update the in flight manuals that describe how to override the system. So, if it happened in flight, there was no way to look up how to override it. Seems like a MAJOR, MAJOR oversight (if true). You can claim all day long that the pilots have "received additional training," but in the moment, when it happens, if the manual in the actual plane has outdated information, what good is that?
There is not a, "Flight manual," carried in an aircraft, there's a QRH - Quick Reference Handbook. The actual aircraft manual (which isn't paper by the way, it's bigger than an encyclopedia set) does contain the information, the QRH does not and should not because that's not where you put immediate actions to be taken. There are two things going on when an aircrew has an abnormal situation:
The first are procedures that are not in the QRH, known as memory items. These are things that the pilot commits to memory and practices in a simulator to ensure they can execute immediately before they reach for a QRH. Examples include the go-around procedure (set TOGA, flaps position, etc.), aborted takeoff procedure, cabin depressurization, and importantly for this discussion, stall recovery is a memory item, as is airspeed unreliable, and angle of attack unreliable. Only once the memory items are completed do they pull out the QRH. When angle of attack is unreliable or airspeed unreliable, the pilots set a specific thrust setting and pitch setting to ensure that the aircraft stays in the flight envelope and in the air. These are things that must be executed immediately and before they can reach for the QRH, and that's why it's a pilot training issue and not a documentation issue. Since November it has been a part of obtaining a type certificate for the 737 Max, but only in the USA, EU, and Japan (nobody else has adopted the FAA EAD as required, as we're discovering now after this latest incident), and the aircrew must show they can execute this before they are permitted to fly the aircraft. Every US 737 MAX crew has completed this training by the end of January to fly the MAX. If you watch, "Sully," Tom Hanks executes several memory items before calling for the QRH.
The QRH contains a series of checklists and is made by each airline, based on manufacturer input. This means that every single airline and aircraft has a different QRH, and for instance an ETOPS 737 would have a different QRH than a non-ETOPS certified 737, on the same airline with an aircraft where every single part is identical. The reason each airline is different is of course procedures for notifying maintenance bases and so on are going to be different, and they may change depending on the routes flown. One noteworthy example of major differences is the QRH between operators for a single engine failure on the 747: since the 747 is technically a 3 engine aircraft (it only requires 3 working engines to be considered safe to fly) airlines have very different diversion and restart procedures based on where they fly and what they fly. The QRH also changes over time based on experience gained with the aircraft. Again, if you watch the movie, "Sully," you can see Tom Hanks call for the non-normal QRH for dual engine loss of power, and they then start the engine restart procedure. You can also watch a documentary on Speedbird 9 which suffered a quadruple engine failure flying through volcanic ash out of Jakarta, which shows the aircrew doing the same - both are examples of excellent crew management and decision making with major aircraft troubles.
Edit to add: AA191 in 1979 is the reason why the EAD is so seriously enforced in the US, but not elsewhere. In that case a faulty maintenance procedure caused the deadliest aircraft accident in US history - but other counties had to learn that less on the hard way, such as Japan with JAL123 in 1985.