> just like in the original trolley problem, the one who pulls the lever becomes responsible for the exchange.

That is a conclusion you can have, but you're speaking like its the official correct conclusion, which isn't really true.

The reason the trolly problem is so popular is because there isn't an agreed upon answer and different people come to different conclusions about it. Some people would agree that by pulling the lever you become morally responsible in a way you aren't if you take no action. Other people think you are morally culpable either way.