"Surely there is such a thing as a piece of code that generates very legitimate warnings, but happens to compile to something that appears to work under at least most circumstances."

Yes. The most trivial example is probably (C++):

  Foo* foo = malloc( sizeof(Foo) ); // warning: void* to Foo*

But this is entirely valid as long as Foo is a POD type, or as long as you use placement new afterwards.

The most annoying warning ever is probably:

  while ( true )  // warning: conditional expression is constant
  {
    foo();

    if ( bar() )
      break;

    baz();
  }

Thanks, compiler! <facepalm>

It's silliness like this which has caused many people to kneejerk ignore every warning ever. But in doing so, they don't realize they're throwing away a lot of free data about their codebase, while also encouraging dangerous coding practices.