The NT itself says that not everything was written down in the NT:
So then, brothers and sisters, stand firm and hold fast to the teachings we passed on to you, whether by word of mouth or by letter. -- 2 Thess 2:15
The sola scriptura believer has to insist that everything St. Paul said "by word of mouth" was later written in Scripture, but by so insisting, he adds his own tradition to what Scripture actually says!
However, the question "is everything needed written down in the New Testament" misses that point. Arguably, "everything needed" is written down in John 3:16. Everything else is just elaboration.
The real question is whether the Bible, in the hands of an individual Christian believer, the ultimate authority over that believer, or is that Bible given to govern the church which Christ founded on his Apostles and gave over to their governance, a church which is a living being, vivified by the Holy Spirit, and hence not needing to be reinvented by each generation by reverse-engineering the text of the Bible.
Pacwa believes the latter. White, in practice, believes the former.