IMHO a .577NE is enough to kill anything. As is your .416 Rigby

However I think that it is pointless to generalise about things and say that such and such will always....

Elephants are living creatures different and individual from each other.

Any boxer will tell you that you can hit some men and it's lights out , some will step back and be dazed, some will walk forward and try to tear your head off.

Some soldiers die on the battlefied from wounds that other men shrug off and win VC's (MOH) continueing fighting till they expire some time later.

Bullet or punch placment is a factor, but some things are just too cussed to curl up and die.

As to the writer saying "a near miss on a elephants brain with the .577 NE, in fact the elephant needed a second finishing shot."
Well a near miss dident hit anything vital. Did he expect the Ele to expire in congratulations of a good try ?