Not true. The apostles appointed authorized successors.
St. Clement, who knew both Peter and Paul and was the fourth pope, wrote this:
“And thus preaching through countries and cities, they appointed the first-fruits [of their labours], having first proved them by the Spirit, to be bishops and deacons of those who should afterwards believe. Nor was this any new thing, since indeed many ages before it was written concerning bishops and deacons. For thus saith the Scripture a certain place, ‘I will appoint their bishops s in righteousness, and their deacons in faith.’… Our apostles also knew, through our Lord Jesus Christ, and there would be strife on account of the office of the episcopate. For this reason, therefore, inasmuch as they had obtained a perfect fore-knowledge of this, they appointed those [ministers] already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry…For our sin will not be small, if we eject from the episcopate those who have blamelessly and holily fulfilled its duties.” Pope Clement, Epistle to Corinthians, 42, 44 (A.D. 98).