If you can't see the libraries in the statically linked program, you aren't looking very hard. The linker copies library functions into the statically linked program, fixing up relocations. This is easiest to see if you compile with debugging enabled, because objdump -d will list the symbol names. Otherwise you may have to resort to looking for instruction sequences or, with LTO, even dataflow graphs.

It's true that there isn't any C in the output of the C compiler, but that's because C is the language your input program is written in; it isn't the program itself.