The EMT should be able to obtain a syringe, fill it with the correct dosage of medication, and then hand it with the vial still sitting on the end of the needle to the paramedic. In this way it can make the medic's job easier, but still requires them to check the Rs before administration. If you're on a scene where you don't have more than one medication in use, the emt can draw up the med, clear out the air, check the dosage, remove them needle, and hand the syringe and vial to the medic to check, so the medic has to do nothing but check the dose, drug, and go.
There's no reason an EMT can't be helpful with medications without causing any danger to the patient or the medic.