Perhaps they should recall tht Joseph was on the way to paying his taxes.
Joseph, therefore, was following the law of the land in which he lived; needless to say, unlike countless others who disregard those same laws and subsequently face the penalty.
And, according to Bill Clinton, Joseph and Mary were homeless.
The whole thing happened within the Roman Empire, which made it possible to dispense with border hassles for a crucial period of history. This wouldn’t be like going from Guatemala to the USA; it would be like going from Georgia to Texas.
I didn’t read article but maybe you are confusing when Joseph went to pay his taxes and Mary Gave birth with sometime after birth when God told Joseph to take Mary and Jesus and flee to Egypt because the king wanted to kill Jesus?
I think/hope the Church is referring to when Jesus and family fled to Egypt. But the church is wrong if they do not point out that the Holy family only stayed while an active threat on Jesus. Once King died they returned to Nazarath.