There is a fairly easy explanation though: The pod the Enterprise was carrying was a prototype without an interface to the ship's systems. It was experimental. It wasn't considered a big deal to require a person inside it because it was easy enough to rig a simple red-alert signal through its communications interface that could warn a person to get out fast.
Or perhaps the pod's instrumentation needed to be calibrated on-the-fly to compensate for the ion storm's effects, and a direct link from the ship to the pod could provide some kind of 'conduit' for the ion storm effects to leapfrog into the ship's systems, so it had some kind of non-networked system that couldn't be controlled remotely, in order to protect the ship. Although if that was the case... why would the pod EVER need to be jettisoned?
Your explanation works in conjunction with the explanation that the pod was a vulnerable extrusion that might even prevent raising shields in its area.
All they really needed to say was that it was an experimental pod. That gives enough wriggle room to suppose it needs to be manned.