Copied from above is the Insight reference involving Clement which the Insight uses as part of the evidence that Peter was not in the "West," including Rome.
*** it-2 p. 622 Peter, Letters of ***
Clement of Rome, though mentioning Paul and Peter together, makes Paul’s preaching in both the E and the W a distinguishing feature of that apostle, implying that Peter was never in the W.
Here is the Clement reference copied with context from here. See if the Clement reference actually makes the point that the Insight gets out of it. (This point, to me, seems like a case of special pleading or grasping-for-straws on the part of the Insight book.)
CHAPTER 5
5:1 But let us pass from ancient examples, and come unto those who have in the times nearest to us, wrestled for the faith.
5:2 Let us take the noble examples of our own generation. Through jealousy and envy the greatest and most just pillars of the Church were persecuted, and came even unto death.
5:3 Let us place before our eyes the good Apostles.
5:4 Peter, through unjust envy, endured not one or two but many labours, and at last, having delivered his testimony, departed unto the place of glory due to him.
5:5 Through envy Paul, too, showed by example the prize that is given to patience:
5:6 seven times was he cast into chains; he was banished; he was stoned; having become a herald, both in the East and in the West, he obtained the noble renown due to his faith;
5:7 and having preached righteousness to the whole world, and having come to the extremity of the West, and having borne witness before rulers, he departed at length out of the world, and went to the holy place, having become the greatest example of patience.