Yes.
I brief them that they can come straight on; I'm going to keep playing on unless we're coming back towards them and it would be dangerous to keep going. If they believe that the game needs stopped, they should just let me know.
Never had an issue with it.
This is exactly how I deal with it and I have found it fairer.
For example, I had a game where the front row went down after the ball had left the scrum, nothing major. Blue hooker for the defending team was screaming blue murder, that I should of stopped the game (he'd been gobby all game) as the FR went down and there was an "injury". No try was scored but territory was gained by Red. Blue hookers's actions were purely to get the game stopped and halt the attack that Red were building. FYI, all the FR were fine, I'm ex-FR and could tell the FR going down was nothing, just a slip. I still kept my eye on it as play went on to make sure nothing serious was building.
I then reminded the Blue captain about our conversation pre-match and to control his players behaviour.
Low and behold, situation was reversed about 10 mins later. Red player was down with a knock. A penalty had been awarded to Blue 10m out from Red goal line. Blue took a quick tap and moved play away from the injured player. Then scored. Cries of from Red "theres an injury sir, the game has to stop". Physio was already on taking care of the player. Funnily enough no uproar from Blue this time around.
Why take away the advantage for the attacking team because there is a minor injury. Play goes on. Physios will soon shout to stop the game. When they come on I'm always keeping it in my periphial vision and if the players shout I don't immediatley stop the game, I look over to where the injury is and see if the Physio is waving at me to stop the game or if the player is clearly in trouble/out cold. Just game management for me