Although I'd like things to behave this way, I don't think this is true. The C standard library was incorporated into the language spec for C89. The behaviors of the named functions within it are specified, and the compiler is allowed to inline it's own version (ignoring your custom code) and then optimize out the inlined portion.
So while it's possible that the external linkage approach still works with certain compilers, it's not portable. I believe you are OK with the external approach if you use a non-standard name (my_secure_memset_pretty_please()), but that just shifts the problem to forcing the compiler to generate your external function without making the same dangerous optimizations.
In the end, I fear you are left with three options: blind faith, non-standard language extensions, or switching to a more secure language (likely assembly). If there are other options, I love to hear about them.
Alternatively, use a library that the C compiler doesn't know so much about that it will attempt to remove calling functions in them.
If you copy your standard library's memset in a separate DLL that is not the standard C library, the compiler will not even see the code during compilation, so it has to compile a function call.
The linker (or a JIT in your C runtime) is allowed to remove calls to the function, if it can prove that it doesn't have side effects. However, to prove that, it has to look at the assembly of the function; it cannot use the way simpler heuristic "it came from <memory.h> and is called memset"