No, words mean things and there is a significant difference between a DOCTRINAL difference and a personal failing.
Had the persecution not happened The Gospel may well have not let Jerusalem.
Poor study of early church history. It was already outside of Jerusalem well before the persecution, starting at the very birth of the church. If something other is what you are "standing" on, it is very poor scriptural knowledge.
As believers fled the persecution they took the message of The Gospel with them.
Believers took the message across the roman empire after Pentecost snipe. Forget to read Acts 2?
Tradition has it before the chosen 12 had died it may have reached as far as Spain.
Most certainly by 90AD it had spread across the empire. So
Ch 8 v1Saul was one of the official witnesses at the killing of Stephen. 2. A great wave of persecution began that day, sweeping over the church in Jerusalem, and all the believers except the apostles fled into Judea and Samaria. 2(Some godly men came and buried Stephen with loud weeping.) 3Saul was going everywhere to devastate the church. He went from house to house, dragging out both men and women to throw them into jail. 4But the believers who had fled Jerusalem went everywhere preaching the Good News about Jesus. 5Philip, for example, went to the city of Samaria and told the people there about the Messiah. 6Crowds listened intently to what he had to say because of the miracles he did. 7Many evil spirits were cast out, screaming as they left their victims. And many who had been paralyzed or lame were healed. 8So there was great joy in that city.
The expansion from Jerusalem came mainly after Stephens death due to the persecution and people fleeing Jerusalem. The Bible say so.