unsafe wiring to shed?
In a word; no.
You would basically have the same situation you do now, except with no equipment ground at all. This is a really common misconception regarding grounding.
The ground rod at the shed does nothing as far as an equipment ground goes. The equipment ground's purpose is to allow fault current, for example from a broken hot wire touching the frame of a power tool, to return to the main panel and trip the breaker. Without it, the power tool will simply have an energized frame, and happily electrocute you.
The ground rod is primarily for lightning protection, to give a lightning strike a relatively safe path to the earth.
Hopefully, the neutral isn't actually broken in your cable, and it was just a horrible mistake on the part of whoever originally wired it. If it is, though, I'm afraid you're going to have to dig.
If it does come to that, I'd suggest burying a 1" PVC conduit instead of UF. That gives you some more options down the road, and will probably last much longer than UF cable.