Certain industries, like air transport, pharmaceutical manufacturing etc have developed protocols for which "RTFM, we explicitly put it in the emergency checklist that yoke pressure won't fix this, so bad on you if you didn't read it" actually is not just a reasonable response but the right one. There's a whole infrastructure of update notices, how updates are published, and a set of protocols for making sure people are up on the latest SOPs (and tracking who is, who is authorized to do X and Y, etc. This bureaucracy is specifically designed to prevent events of this type.

Hell, every aircraft is slightly different and the pilots and/or service people don't treat them as such (although in practice typically the differences may be negligible for the pilots -- but they will check).

So based on that it is absolutely the airline's responsibility to make sure that the people operating any equipment are checked out on it.

So it is possible (though pretty unlikely) that Boeing failed to follow their protocol, e.g. didn't send out the right notices on a timely bases or something, and if so they would be responsible. But with all the airframes they've shipped over the decades that's pretty unlikely.