I do take injuries while power training, but I do use hard training and don't pump green packs into them until the bar goes orange (sub 40%).
However, during matches I take far more injuries than my opponents. The ratio so far this season is 5:2 (10 to 4 total from matches). My starters are all 6* and above with max condition and superb morale for all matches. It hasn't made much difference with the injuries, and several of those dropping aren't immediately following a day of power training.
I've also used hard tackling on all my matches both this season and last. From all matches (including friendlies) opponents have suffered just 7 injuries (roughly 75 matches), while I've suffered 19. In my opinion, there is something fishy with the injuries in this game.