That's just simply not a realistic expectation for the ED. If the ED is short a nurse the ED needs an ED nurse to handle the patient load, not a "runner" floor nurse who would "help" an ED nurse because regardless of what extra help that floor nurse does, the ED nurse is ultimately responsible for those patients since that floor nurse cannot be independent. Instead of getting an additional ED nurse to split the assignment, getting a helper nurse to do tasks will not benefit anyone. That is why the nurse who protested getting sent to the ED was within her rights to do so. It's also why (safe) ED's go on divert mode when there's staffing issues instead of plucking from the float pool or pulling from any of the other med surg floors because their level of training and education are not the same as the skillset required of an ED nurse.
I'll give you an example - when I worked med surg, we did not draw labs - phlebotomy did that. If I had been floated down to the ED, I wouldn't have been able to "help" the ED nurse with that. Furthermore, my med surg mindset would go looking for a pump to hang IV antibiotics, never knowing that in the ED, with the exception of Vanco, everything is hung by gravity. if someone told me to go get "Bair Hugger" I wouldn't even know where to begin cause I wouldn't even know what it was since we don't use it on the floor. And would you really expect a floor nurse, who goes to work every day to the same floor, know where MRI/CT scan/XR/etc are to even transport patients? So the assumption that a nurse is a nurse is a nurse is not safe, and downright wrong, even if it's just as a helper nurse to a specialized floor, which the ED is. And that's pretty much what happened in this case with the Versed. That nurse who gave it had no idea what she was giving. And she too was "helping".