Who says the ground is open? How did they determine that?

"cause a fuse to blow on a water well circuit?"

No.

But, it's a very bad thing and needs to be repaired.

the ground wire just under the well cap was stuck (barely)under the wire nut but came right out when I pulled on it. It has been repaired.

That ground wire, if correctly installed initially, is not the one grounding the pump-- which I assume to be a submersible. But the ground wire for the pump, in and of itself, whether intact or broken, would not cause a fuse to blow.

If it touches a bare hot lead or contact, it'll blow.