System headers before other headers according to Google Style guide?

Question

I was playing with cpplint and I got this warning:

Found C++ system header after other header. Should be: transpose_square.h, c system, c++ system, other.

The source is the Google Styleguide, that apparently says (said?)

1. associated .h/.hpp (if this is a .cpp file)
2. C system files
3. C++ system files
4. Other libraries' .h/.hpp files
5. Your project’s .h/.hpp files

Leaving aside 1., I honestly thought that the recommended order was exactly the opposite!

2. Your project’s .h/.hpp files
3. Other libraries' .h/.hpp files
4. C++ system files
5. C system files

So, basically the idea is to include the headers in the order of "increasing distance" from the current project, ending with the most basic libraries.

I don't remember where I took that from, but I remember the logic was to detect missing dependencies headers in related or in the same project.

I don't remember if there was more than just this.

For example, in this case, the order will be forgiving for text_processing_utilities.hpp to have a missing #include<string> even if it depends on it:

#include<string>
#include "text_processing_utilities.hpp"

My question is, is the Google Style guide for headers a good convention regarding the order of system headers? Is there a good reason for it?