Even a max pull- up at LKP should require 20 - 30s before stalling the plane (at that point I assume it was not yet in Alternate 2 which might allow for an accelerated stall). Stalling should happen somewhere around 350 kts ground speed. At that point it will already have travelled ~4nm and it will still be traveling at that speed.
Henra, just imagine you could pump the stick while in direct law in time with the aircraft's short period oscillation. Don't you think you could amplify the aircraft's pitching motion until the aircraft stalled in just a few cycles? Particularly with a C.G. almost at the aft limit, it would be easy. That is a dynamic departure from controlled flight, and it can be done in just a few cycles.
Now just imagine that the aircraft is flying in Normal law, on autopilot and with autothrottles and something causes the motion of the control surfaces to slow down so that they never get to the commanded position before the signal reverses. The control surface itself does not begin to reverse direction until its position signal crosses the command signal. This happens significantly later than the command signal's order. The result is like the F-22 prototype that encountered PIO on a go -around.
The something that delays/slows down the control surface is called control rate limiting, and it is a known cause of PIO. Do you see that what you may have learned about the aircraft's control system may not apply in special circumstances like control rate limiting?