Wether he arrived with Winthrop or not is not relevant to our definition of PGM. He need only have arrived between 1621-1650. Clearly if he was here in 1638 for the land division, then he was here before 1650, and was not born here, so immigrated after 1621. So definitely PGM.
As for Cutter, I only believe him, after I've double checked his information. But someone else may have said so before Cutter, and someone may have stretched the truth. And I don't think the online lists are complete.