Even the Catholic Church admits they can’t prove that.
As to the duration of his Apostolic activity in the Roman capital, the continuity or otherwise of his residence there, the details and success of his labours, and the chronology of his arrival and death, all these questions are uncertain, and can be solved only on hypotheses>/b> more or less well-founded.
Uncertainty and hypotheses are not the basis that I am relying on for my salvation and beliefs.
Source? My source is in the links I posted up at the top.