I would argue that since the method is deliberately left unclear, in reality it mostly profits to whoever wants to game it to his/her advantage. And if everybody wants the project to succeed as their respective primary goal, then you do not need such methodology anyway.
Do whatever seems to work best for the team, and don't name it. Don't waste time writing blog posts about how you found a new groundbreaking way to work, as these matters are subjective.
For example, now I work by asking whatever needs most attention right now, getting it done, and then asking again. No backlog, no notes anywhere, nothing. If we forget about something and it is important, it will come back up. It has no name and it works perfectly for us!