Here is my view.

There is nothing wrong with 'transfer responsibility' and it does not make dandelion's sentence in the original post so grammatically incorrect (I would probably say "transfer responsibilities" if I were to say it). In that sense, you are absolutely right.

However, in the context of his sentence/post, I would think it is not the best choice of words. He probably meant to say "shift responsibilities to you", if not totally "scapegoat you". Well, I could be wrong as it is just my understanding. I hope I am not second-guessing dandelion, or anyone.