That is not the stated purpose of the tool (to write code in the aforementioned style):

  "Include what you use" means this: for every symbol (type,  
  function variable, or macro) that you use in foo.cc, either 
  foo.cc or foo.h should #include a .h file that exports the 
  declaration of that symbol.

I agree 100% with that statement. According to the style, foo.h can never #include anything.