Maybe Rand's white mice escaped? With a degree in maths and another in astrophysics it was take a job as Kirk's yeoman or the dole queue again on Monday morning.Probably because it was cheap to use a globe (cloudless, no less) -- they used it again in "Tomorrow is Yesterday".
That said, I like it a LOT. It's not kind of Earthlike. It's not Class M. It's Earth. And we actually see that globe again, though it's often disguised with colored haze (and sometimes reversed).
My rationalization is that there are lots of parallel Earths scattered around the galaxy. Maybe constructed, maybe fractures of a kaleidoscopic creation. And that's why there are so many humanoids around. The "Preservers" theory is not contradictory to this idea.