Code J simply means that the distribution was paid to you and you were under age 59½ at the time. You could have rolled it over unless you had rolled over another IRA distribution made within the one-year period ending on the date of this distribution. Perhaps what you were told was that it was not possible to do a nonreportable trustee-to-trustee transfer, but that would not preclude you from rolling this distribution over within 60 days of the distribution.
