Paul didn't write 2 Tim. Check this page :2 Timothy That site represents rather mainstream scholarship. There are much more radical scholars that rightly call into question many of the assumptions plaguing the research, but its a fine introduction to where real scholarship stands.
But the point your making is valid. Ironically the author refers to Jannes and Jambres as a scriptural bad example yet they are not mentioned in the writings that were finally canonized as the OT all but were very well known through tradition and apocryphal writings. Clearly the WT is missing something.