That's why having neutral trainers come out is the best idea I've seen.
We have refs to call penalties who (supposedly know the rules) and (supposedly) call things fair. Perfect? No. But lots better than calling your own penalties.
Same with injuries. A questionable injury is currently "self reviewed" which is like "self called" penalties. It doesn't work but you can't just arbitrarily say "all injuries are the same and deserve the same amount of time out of the game" just like all penalties aren't the same.
It just makes sense to have someone neutral judging the injuries since teams are trying to get an advantage, just like they do with penalties.