Instead of calling it 'The Rule of Three', call it WET (Write Everything Twice); makes it easier to remember (although I think that is one less repetition than suggested in the parent.)
Our industry is full of dogma and false prophets. It’s unbelievably frustrating.
Interestingly, I just looked at the wikipedia page for DRY (https://en.wikipedia.org/wiki/Don%27t_repeat_yourself) and see they also mention another acronym - AHA (avoid hasty abstractions); I might use that in the future.