I believe he was right, because the first letter, bearing a certain date from Pietra Santa, was written in March 1518 to Pietro Urbano.

It contains the account of Michelangelo's difficulties with the Carraresi, and his journey to Genoa and Pisa.

We have, therefore, every reason to believe that he finally abandoned Carrara, for Pietra Santa at the end of February 1518.
Pietra Santa is a little city on the Tuscan seaboard; Serravezza is a still smaller fortress-town at the foot of the Carrara mountains.
Monte Altissimo rises above it; and on the flanks of that great hill lie the quarries Della Finocchiaja, which Michelangelo opened at the command of Pope Leo.

It was not without reluctance that Michelangelo departed from Carrara, offending the Marquis Malaspina, breaking his contracts, and disappointing the folk with whom he had lived on friendly terms ever since his first visit in 1505.

A letter from the Cardinal Giulio de' Medici shows that great pressure was put upon him.
It runs thus: "We have received yours, and shown it to our Lord the Pope.