Don't blame the crew here, but the system.
If the captain is adding a nose-down input of his own while the first officer is PF, then he should push the take-over button to disconnect the F/O stick and take full control himself.
The sidestick/FBW system is not designed for 'corrections' to be made from the opposite sidestick, hence the 'dual input' warning being incorporated in the first place.
A small point, but worth mentioning when discussing how the crew reacted.