So, here are the results of my technical investigation:

The library we use to render 3D objects requires that vertical rotation be between 0 + .000001 and pi - .000001, presumably because of some mathematical assumptions they are making that I don't fully understand. Because I would need to cram what I assume is a graduate-level linear algebra course in order to understand, much less alter, their system, I think it is probably not worth our time to pursue this further. However, I could attempt to provide a hack if this is still thought to be worthwhile...it just may not work very well.

Let's avoid a hack. We should file a bug upstream, I think. @MarkTraceurand @Gilles do you know if there's any bug filed upstream on this at https://github.com/mrdoob/three.js/issues ? I tried some searches and it wasn't readily apparent to me if it had been filed upstream.

It seems to be configurable: https://github.com/mattdesl/three-orbit-controls/blob/master/index.js#L39

@Gilles nope - when I change those variables to, e.g., Infinity and -Infinity, the only change is that rotating past the poles will make the camera freak out. I also tried adding in a "restrictPolarAngle" configuration, and not checking the angle in that case, but it didn't help.

It's probably a bug/untested behavior in three-orbit-controls then. But doesn't sound like a bug in threejs per se (the trackball controls don't have that limitation, for instace). You're free to write your own controls plugin, fork this one, etc. There might be other options out there too, I see that the examples folder in threejs has a different version of this one, I'm not sure which one is in use for the extension.

Yeah, I think it's still worth asking whether we really care about this limitation, but if we do, then I'll pursue looking at another control scheme.