Is the Syntax of C Language completely defined by CFGs?
The C language has typing rules. For example, you can't divide two pointers, and when you call a procedure accepting a pointer, you can't use a double. A C compiler analyzes its source in several phases: first there is lexical analysis, then the source is parsed, and so on. These phases are abstraction, and in fact additional information is passed from phase to phase. For example, even though the grammar of C doesn't care about names of variables, this information is passed, and that's how the attributed grammar can verify the typing rules. So there are additional mechanisms working on top of the grammar.

For an even simpler example, take the one given by Aho and Ullman. At the parsing phase, all variable names look "the same", yet you cannot use a variable unless it had been declared. This information is hidden from the context-free parser, but is retained as an attribute for the lexical phase, and is checked during parsing. The context-free grammar of C represents only some aspects of what legal C code is, which are useful for implementing a fast parser. On top of that parser, the other rules are checked, semantics are given to the C code, and machine code is generated.