The IIIc was a wartime camera and parts were not so readily available from Germany. In fact the IIIc never reached (meaning imported and sold in) Britain until long after the war apart from captured/liberated ones. So other cameras' parts were cannibalised to keep them all going and so on.
Some wartime camera magazines here had articles about captured IIIc's which they thought were IV's only Leitz stopped the Roman numbers at 3 for some reason I've never understood. (So you get the old and new (die cast) as variations of the III's, weird... It seems sensible to call the die cast versions IV's, but there you are.)
Anyway, that might explain how a IIIc became a unique Leica BITSA*.
Regards, David
* Cultural Note; the word BITSA is a corruption of "bits of this and bits of that" and was in widespread use once upon a time