It does make sense..perfect sense. Although, I think Ford could have done a better job diagnosing the issue.
The voltage dropping too much results in degrading operation of various circuits, the most noticeable is the VCT, and hence the sensor malfunction codes. It doesn't take that much of a drop in DC, to around 12.5-12.8 volts, for the codes to get thrown. Normally the alternator is putting out roughly 14v dc.
If you're car is running bad w/o codes, then you likely have fouled plugs, a dirty maf, or dirty throttle body.