Looks like different types of safety sheaths are being discussed here, so of course you're going to get different answers.
Our newer insulin syringes have a sliding, translucent "tube" cover that, once the med is drawn up, you are to slide up to shield the needle for transport. Yes, I suppose you could do some weird trip-fall-untwist the shield-stick yourself, but it's hard to picture that, you know? Upon arriving at the patient's side, it's quite simple to slide down the sheath and inject, sliding it back UP to dispose.
On the other hand, we also have needles that have a safety sheath that is designed to be "locked on" after an injection is given, prior to disposal in the sharps box. That said, the ONLY time that actually occurs is when someone gives an IM, which is pretty rare on our floor, or rarer yet, a sub-q that is not manufactured in advance (like Lovenox or Arixtra, that have self-locking syringes).
The great majority of the time, if using one of these needles to draw up into the syringe, we slide up the safety lock/sheath and transport to the patient, where we use our needless IV system to deliver the med. Meaning, twist off the whole needle, locked as it is, give the med, and toss both parts in sharps. No issues or controversy.