As soon as I had noticed it, I went to complain to the driver and he just disclaimed liability.

liability 是名词，由形容词 liable（有责任的）加上名词后缀 -ity 构成，表示"责任、义务"的意思。在法律语境中特指"法律责任"。 disclaim liability 是一个固定搭配，disclaim 表示"否认、拒绝承认"，整个短语意思是"推卸责任"或"拒绝承担责任"。