Based on Japanese social history that is possible, but the choice is between testing for thyroid cancer and risking social ostracism or not testing and possibly dying from an undiagnosed cancer that is highly treatable.
The survivors of Hiroshima and Nagasaki included large numbers of victims who had burn scars and other visible injuries. That will not be the case with the people exposed to radiation from Fukushima. Thyroid screening is non-invasive and would seem to be easily kept private. Further, I would hope that the Japanese have learned from the past. In any case, based on the lessons learned at Chernobyl, I would want my children tested.