Exactly. As I have heard it, they originally tried to sell their big developers (e.g. Adobe) on total rewrites for Rhapsody/NS/Cocoa and were more or less laughed out of the room. Carbon was a compromise.
I don't think the evolution of C vs ObjC APIs was a good proxy for the future viability of Carbon vs. Cocoa. If an API was intended for Carbon apps, it had to be C. If it was exposing core OS services already implemented in C, it was more likely to be C. Even fairly new APIs like Grand Central Dispatch have both C- and ObjC-intefaced components, based on the level of abstraction.
I also seem to recall (though I'm not an expert and I certainly don't have inside knowledge) that in those first few releases both Cocoa and Carbon were evolving, sometimes at different rates in different areas. Then I remember when Core Foundation and similar C-only APIs became a thing that people talked about, which as an onlooker of the platform kind of confused me at the time - was it an admission of some inadequacy of objc?