enums and switch vs function calls

If I have:
enum colour {RED, GREEN, BLUE}
int colour_to_hex(enum colour colour)
{
     switch (colour)
     {
         RED: return 0xff0000;
         GREEN: return 0x00ff00;
         // BLUE: return 0x0000ff;
     }
     ...
}
... then the compiler will warn me that I've missed a case in the switch statement.  Which is good and very helpful.
But if I do:
int hex = colour_to_hex(10);
... then the compiler doesn't complain that 10 is not in the enum.
Why? Surely the compiler can tell.