Spot on John, fuses are an often overloooked source of problems. Going back to the days of "Continental" ceramic (and later, plastic) fuses, they were almost guaranteed to give trouble.
Then blade fuses arrived and were much more reliable. However i've had many problems over the years with blade fuses, either the blades corrode causing a problem when they warm up and effectively disconnect the circuit or the fuse holder itself has overheated (usually as a side effect of the fuse corrosion) and melted the fuse holder. This extrapolates to all fuses to a greater or lesser degree so i totally agree with your analysis. The one point against it is that interior lights are a relatively low current draw so will drop less voltage over a resistive joint.
As you allude to, it may still be the battery but could also be a poor connection, the lack of any electrical activity points to a general connector which is more likely an earth rather than a fuse if all circuits are down.