Regardless of the verity of that account, it is a fact that Aritsuna served as a loyal commanding officer under Yoshitsune, and even after Yoshitsune came to have a conflict with Yoritomo, Aritsuna was a member of the group that accompanied Yoshitsune when he left Kyoto.
そのことの真偽はともかく、有綱が義経の忠実な部将として行動したのは事実であり、頼朝と義経が対立した後も都を落ちる義経の一行に加わっている。