He's talking about the chords build upon those scale degrees in the parallel minor key, not the scale. Don't think about the key of F major. He's only talking about the keys of G major and G minor. So each time he shows a chord symbol at the top of the staff he's indicating what chord it is not the key.
So a chord built upon the third scale degree of G minor is Bb major. If you build a chord on the seventh scale degree of G minor you get F major. He's making an assumption about "generic" sound based on his own experiences.
When notes and chords are "borrowed" from relative major and minor keys, it's usually done to change color or add interest. The composer chose to do these things to achieve a sound more interesting than using just G major.
I hope that helps in your understanding.