That is correct, yes. You can limit the scope of a function to a single file using the static keyword; otherwise all functions are in the same global namespace for static linking.
In practice, this is not a big limitation by itself. Although C has function pointers, it's not a functional programming language -- there are no closures, and you can't create new functions at run-time under any circumstances. (Not within the language itself, anyway. You'd need to embed a compiler, or at least a minimal code generator.) On Harvard-architecture systems like microcontrollers, code and data may be in different memories (ROM vs. RAM) with different access permissions, and some platforms even put them in entirely separate address spaces.
In practice, this is not a big limitation by itself. Although C has function pointers, it's not a functional programming language -- there are no closures, and you can't create new functions at run-time under any circumstances. (Not within the language itself, anyway. You'd need to embed a compiler, or at least a minimal code generator.) On Harvard-architecture systems like microcontrollers, code and data may be in different memories (ROM vs. RAM) with different access permissions, and some platforms even put them in entirely separate address spaces.