This recording from a Greek Second Division game shows exactly why you don't want to be injured when these particular medics are on hand.
Ergotelis midfielder Leonardo Koutris was suffering from an injury in the match against AE Larissa when the medics rushed onto the pitch, but were seemingly unable to agree on how to carry him off. After a bit of arguing, they were seen carelessly tossing him into a stretcher.
Then, looking like a scene from Fawlty Towers, the pair ran off to get Koutris some help... but dropped him. And fell on him. Then dropped him again.
Once they finally managed to reach the sideline, they simply dropped Koutris to the ground.