The aircraft was at 3000', skirting some wx and in cloud and rain. GPWS went off, and although there's only 400' to MSA, you MUST follow the procedure, and once you've got GA thrust set and 20 deg nose up, you ain't gonna stop it in 400'! If you did you'd be peeling people off the roof! There's no exception where you can trickle the thrust on and climb to MSA! Besides, if the GPWS is going off you can't trust your altimeters!
ATC advised QF of conflict and they turned, they could see the NZ aircraft on their TCAS, and it turned from blue to red, but they never got a RA. The climb wasn't intended to 5000', but once the appropriate procedure was followed that was what they had.
It looks like a spurious GPWS at this stage, possibly due to the rain.