I may not have explained this very well. The essential idea is being examined is the proposal that one doesn't have a single low probability event but a series of low probability events that must happen in serial after life arises even as there are chances for each happen in parallel (say , multicellular life, development of neurons or equivalent, development of writing, etc.) In that case, most civilizations should show up around the long-lived stars as long as the others issues are only marginally unlikely.

Thus, the tentative conclusion is that life itself isn't that unlikely and we find ourselves around a star like the sun because they have much bigger habitable zones than red dwarfs (or for some similar reason) so the anthropics go through as your last bit expects.