Anyone know why setting Case.Status inside a loop using format() works, while attempting to set EmailMessage.Status inside a loop using format() fails?

System.DmlException: Insert failed. First exception on row 0; first error: INVALID_OPERATION, operation is not allowed: []

public class testingForLoopProblem {
    public testingForLoopProblem() {}

    @isTest static void Case_ForLoop_Success_Test() {
        Account acc01 = new Account(Name = 'success');
        insert acc01;

        Integer NUM_RECORDS = 6;
        List<Case> cases = new List<Case>();
        for (Integer counter = 0; counter < NUM_RECORDS; counter++){
            Case caseTemp = new Case();
            caseTemp.AccountId = acc01.Id;
            caseTemp.Subject = 'Test: : ' + counter;

            // Why does this work?
            caseTemp.Status = counter.format();

            cases.add(caseTemp);
        }
        insert cases;
    }

    @isTest static void EmailMessage_ForLoop_Fail_Test() {
        Account acc01 = new Account(Name = 'fail');
        insert acc01;
        Case case01 = new Case(AccountId = acc01.Id);
        insert case01;
        Integer NUM_RECORDS = 6;
        List<EmailMessage> emails = new List<EmailMessage>();
        for (Integer counter = 0; counter < NUM_RECORDS; counter++){
            EmailMessage email = new EmailMessage();
            email.ParentId = case01.Id;

            // Why does this NOT work?
            email.Status = counter.format();

            emails.add(email);
        }
        insert emails;
    }
}

 API Version 27.