This is very interesting. I never heard/thought about this.
If I understand correctly, even if your friend actually said "行かない" if you wanted to quote them directly you would say "行きません"?
What if you wanted to quote them accurately including their tone.
For example, if your friend actually said お前は馬鹿野郎 and you wanted to quote them you would say
友達は「お前は馬鹿野郎です」と言いました?