I personally think any instance where a player stops the game because of an injury should result in a substitution, HIA or a green card regardless of whether the game is stopped by the referee or a club doctor. Anyone stopping the game for a head injury should result in an automatic HIA assessment. If contact to the head is bad enough for it to stop the game then it requires a HIA.
I'm sure I saw in a game this weekend (I believe it was Warrington), the Doctor or physio saying a player was fine to play on following a head injury, the ref stated that it would then be a green card, so the Doctor or physio changed his mind and advised the player would go off for a HIA.
I would also scrap the video ref reviewing foul play. If a player knows they won't get a player sent off following the incident, they won't stay down.