Jesus made several references to the persecution and martyrdom of the prophets (Mathew 23:29-37; 21:35; 22:6; 5:12; Luke 6:23; 11:47) which are not found in Old Testament (with some exceptions like 2 Chronicle 24:21), but found mostly either in Jewish tradition or in apocryphal/apostate literature. He had no problem in talking even with Satan himself. (Mathew 4:1-10)
Jesus is not an exception. Jude too makes reference to things that is not found in Old Testament (Jude 14-15).
This obviously means the faithful servants of God had no restriction on reading things not inspired! Yet JWs are told not to read apostate literature!