It is not biblically shown that Peter was never in Rome.
I can tell you without doubt where it IS biblically shown that Peter traveled to..1.Caesarea, in Palestine. (Acts 10:24). And 2. Antioch in Syria. Where the Bible says he was warmly welcomed by the people and patted cheeks of children and blessed all the faithful.
No. Wait...it doesn't say that at all. It says that rather than having ANY MINISTRY THERE, Peter was REBUKED by Paul. (Gal. 2:11-14).
The hard biblical FACT to accept for the RCC is that Peter and the 11 ministered in Palestine only. (Acts 10:39, 21:17-20). And there IS a reason for this. Read Acts 8:1 for a start. "And Saul was consenting unto his death. And at that time there was a great persecution against the church WHICH WAS AT JERUSALEM; and they were all scattered abroad throughout the regions of Judea and Samaria, EXCEPT THE APOSTLES.". Until Israel, as a nation is set aside, in Acts 28, the apostles remained in that area, ministering to the Jews. And waiting for them, as a nation, to accept Christ as their Messiah, so He could return and set up His Kingdom, where they will reign with Him, on twelve thrones, judging the twelve tribes of Israel.
That's what the Bible says. If you're interested..