Did anybody even claim that herd immunity is about immunity being “transmitted” from one person to another? You spend some time in your article arguing against that, but it’s a straw man. I don’t think anyone credible believes it or has proposed it.
The point is that herd immunity occurs when there are enough immune people that a virus finds it hard to spread, and therefore has a much lower chance of ever reaching the non-immune people.
Moreover, herd immunity is not defined as necessarily involving vaccination. Obviously a large-scale vaccination programme will speed it up and might virtually guarantee it, but it can occur naturally.