Safety campaign group Progressive Rugby claimed the HIA protocols had been "exposed" after Johnny Sexton was passed fit to play in Ireland's second Test against New Zealand.
Ireland skipper Sexton was taken off with a head injury during last weekend's first Test, but he passed the subsequent HIA checks and was given the all-clear to play again on Saturday.
Responding to the criticism, World Rugby said in a statement on Thursday that the wellbeing of players is never put at risk.
"It is the duty of any individual or organisation commenting on the head injury assessment process to do so using the facts," the statement read.
"Attempting to diagnose a serious medical condition like concussion from afar, without all the relevant information including a player's medical history, is irresponsible and no substitute for the world-leading medical care received by elite rugby players.
"Doctors are supported by the head injury assessment and recently updated return-to-play protocols put in place by World Rugby.
"These protocols are developed using scientific evidence and independent expert opinion which are kept under constant review, as we never stand still on player welfare."
As part of changes announced by World Rugby last month, players now face an increased minimum period of 12 days out of action should they be found to have suffered a concussion.
That has seen the likes of Tom Curry and Tomas Francis return home from England's and Wales' tours of Australia and South Africa respectively this week after sustaining such injuries in their opening Tests.