> The Simple Rule
> If the Friday you’re referring to is beyond seven days from today, including today, it’s next Friday.
That's not a such simple rule. I'm not even sure what "including today" means.
A simple rule would be: next Friday is the first Friday after today.
The whole existence of this website suggests that the term "Next Friday" is at best ambiguous. Especially on a Saturday or Sunday, many people will interpret "Next Friday" as the Friday of next week. So just be explicit and say "Friday next week".