I've heard this explanation many times, but it seems many times western Easter Sunday falls after the first day of Passover, yet the Orthodox still celebrate Easter a month later. I suspect the explanation is much more complicated.
The regulations of the First Ecumenical Council concerning the calculation of the date of Easter were handed down to us by the Council of Antioch in 341 A.D., which had received the decision concerning Easter from the First Ecumenical Council. This is also corroborated by the testimonies of Athanasius the Great and St. Epiphanius of Cyprus.
These regulations of the First Ecumenical Council are as follows:
1. "That Easter must always be celebrated on a Sunday".
2. "That Easter must never be celebrated on the same day as the Jewish Passover".
3. "That Easter should never be celebrated on or before the vernal equinox of any year".
It should also be noted here, that Cyril the Patriarch of Alexandria, in his Paschal Circular, stated:
"The Ecumenical Council unanimously voted that the Church of Alexandria, because of its noted astronomers, would announce to the Church of Rome every year the date of Easter, and Rome in turn would announce it to the other Churches".