You are correct in that lack of nose-down pitch often goes together with a tendency to develop a 'locked in' stall if recovery action is not taken promptly.
Just to be clear. This accident did not involve a locked in stall. The aircraft had recovered from its stall on the way down and accelerated to very high speed.
For some reason, the crew did not recover from the resulting spiral dive. The wings were not leveled which is the first step in recovering from this type departure.
Application of g while wing down-nose down just winds the spiral tighter.