And, as I pointed out before and in spite of the fact that this plane is not technically fly-by-wire, the computer interposes itself between the pilot and control surfaces in a myriad of ways so taking 100% manual control is rather more complicated than pressing a single button.
You have said this, and I'm pretty sure it's not correct in any
operational sense in any Boeing airliner. Disconnecting the AP is indeed a single button push -- and that button is on the yoke, too, right where it can be pressed in an instant. The plane can also adjust the trim automatically, and as the AD makes clear, that can also be turned off. But even if not turned off, it can be overridden by the pilot's controls without any special action other than pushing or pulling harder than usual. Similarly, there's an trim and automatic yaw damper on the rudder which the pilot can disengage, but he can also kick the rudder however he wants and the machine will obey.
Boeing has aircraft such as the 777 that have FBW, but their philosophy is quite a bit different than Airbus's. The machine will essentially inform the pilot that he is about to exceed the aircraft's envelope by making it increasingly difficult for him to assert his control input (by pushing back against his inputs), but it will not override him. Check out section 11.3 of this document:
http://www.davi.ws/avionics/TheAvionicsHandbook_Cap_11.pdfSo, though there are systems (electric, hydraulic) between the pilot an the control surfaces, the pilots commands ARE obeyed unless something has actually broken.
This is totally different from an Airbus aircraft, where the computer under "normal law" enforces the flight envelope no matter the control inputs. There are several other modes the aircraft can be in, such as "alternate law 1" where the plane continues to enforce most of the envelope except AOA and overspeed, and "alternate law 2" where only load factor is enforced, and of course "direct law" which is basically "you're on your own kid."
In this case, it looks like the computer might have pushed the nose down, but the pilot could have counterracted that with the normal controls, albeit, with extra force.