"But you may what to watch because a tri-tone can exist in a IV chord as well (#4). The subdominant name given to that chord is just music terms in the least."

Sorry, I don't agree with that. Once a tri-tone is introduced, the chord becomes dominant. Albeit secondary, but a dominant, nonetheless, with it's own resolution properties. Example: C7 F7 G7. Even though it is written in C, the only actual chord in C is G7. C7 F7 G7 is nowadays, considered a I IV V progression, just for simplicity. It is not technically. There are no semantic rules or arguments or music terms to deny that fact. The reason the IV chord is called the subdominant is simply because it's below the dominant. Adding a tritone to any chord, for that matter, changes the function.