You've confused what that sentence is. It is not permission to always make a specific object interaction (drawing a weapon) as free with a specific action (attacking).
It is an example of something that is a free object interaction (drawing a weapon while attacking), followed by the requirement for the Use an Object action, including for a second (not free) object interaction. If you've already taken a free object interaction, then that section is specifically telling you that you *don't* get to draw a weapon with your attack for free, even though it normally would be free. You've got it back to front.