Outlet tester results for open ground on mixed circuit
You're about correct on the ground wire being floating loose at the other end

The other end of that ground wire is indeed most likely floating loose; this is OK if the outlet is GFCI protected, though, as the GFCI will trip and save you if something plugged into it tries to bite you.

As to the NCV tester...

Since the neutral is bonded to ground at the main panel, a normally functioning neutral will not light up a NCV tester (you can test this by sticking the tip of the tester into the neutral slot on a normally wired outlet).  It's neither a problem with the tester, nor the outlet.